In this paper, we use Monte Carlo simulations to compare parametric estimators of Type 1 Tobit model. In particular, we examine the performance for finite samples of three different estimators of simple Tobit model: t...In this paper, we use Monte Carlo simulations to compare parametric estimators of Type 1 Tobit model. In particular, we examine the performance for finite samples of three different estimators of simple Tobit model: the least squares (LS) estimator, the Heckman (H) estimator and the maximum likelihood (ML) estimator. These three estimators are consistent and asymptotically normal in the case where the density error is specified. However, these properties are sensitive to the situation where the error distribution is not specified. The purpose of this article is to determine properties of the three estimators, namely bias and convergence, by using Monte Carlo simulations.展开更多
In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has b...In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.展开更多
This paper is an extension of Hanif, Hamad and Shahbaz estimator [1] for two-phase sampling. The aim of this paper is to develop a regression type estimator with two auxiliary variables for two-phase sampling when we ...This paper is an extension of Hanif, Hamad and Shahbaz estimator [1] for two-phase sampling. The aim of this paper is to develop a regression type estimator with two auxiliary variables for two-phase sampling when we don’t have any type of information about auxiliary variables at population level. To avoid multi-collinearity, it is assumed that both auxiliary variables have minimum correlation. Mean square error and bias of proposed estimator in two-phase sampling is derived. Mean square error of proposed estimator shows an improvement over other well known estimators under the same case.展开更多
The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estim...The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.展开更多
AGB (aboveground fresh biomass) is one of the most important parameters of the crop condition monitored with remote sensing. Hyper spectrum remote sensing with the fine spectrum information becomes the efficient met...AGB (aboveground fresh biomass) is one of the most important parameters of the crop condition monitored with remote sensing. Hyper spectrum remote sensing with the fine spectrum information becomes the efficient method estimating the vegetation AGB. The research was conducted in Xinjiang, the largest cotton planting region of China. The paper analyzed the correlation between the cotton AGB and reflective spectrum and the first derivative spectrum, and the variation coefficient of the waveband reflectance. According to the analysis above, all of 23 parameters, including the hyper spectrum reflectance, the first derivative spectrum parameters and normalization vegetation indexes, were established. And then the estimation models on cotton AGB of relaxing and compact canopy type were established and tested respectively. The tested results showed that Fgo1, [901,502], [901,629], [901,672] among the reflective spectral parameters and D525, D956, D1019, D1751 among the first derivative spectral parameters had the homogenous effect on different cotton canopy types, and the determination coefficients of the models above all arrive at the significant level of 0.99 confidence interval. At last, the tested results of the homogeneity models for different canopy types indicated the parameters of [901, 502], [901,629], [901,672] have more satisfying veracity than others, and the relative errors are as low as 17.0, 16.3 and 16.7% correspondingly; in contrast, the estimation veracity of the first derivative spectrum parameters of single waveband is low.展开更多
In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the metho...In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.展开更多
Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation a...Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial frequency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively; and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].展开更多
Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associa...Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.展开更多
This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme,...This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.展开更多
This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown p...This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown parameters under a squared error loss function. The approximate Bayes estimators will be computed using the idea of Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions. Also the point estimation and confidence intervals based on maximum likelihood and bootstrap technique are also proposed. The approximate Bayes estimators will be obtained under the assumptions of informative and non-informative priors are compared with the maximum likelihood estimators. A numerical example is provided to illustrate the proposed estimation methods here. Maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo Simulation展开更多
Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available f...Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme. Bayes estimators have been developed using the standard Bayes and MCMC methods under square error and LINEX loss functions, using informative type of priors for the parameters. Simulation comparison of various estimation methods is made when n = 20, 40, 60 and censored data. The Bayes estimates are found to be, generally, better than the maximum likelihood estimates against the proposed prior, in the sense of having smaller mean square errors. This is found to be true whether the data are complete or censored. Estimates improve by increasing sample size. Analysis is also carried out for real life data.展开更多
The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the probl...The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.展开更多
For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2)...For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2),Weak L^1(R^2).This extends the theorem of Stein & Wainger and the theo- rem of Weinberg.展开更多
In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the ma...In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters. Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators. Numerical examples using real data set are presented to illustrate the methods of inference developed here. Finally, the maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo simulation study.展开更多
In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application ...In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.展开更多
Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteri...Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient.By designing an appropriate vector filter,phase velocity,attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array.Performance analysis of this algorithm is compared with Extended Prony Method(EPM)and Forward and Backward Matrix Pencil(FBMP)method.Based on the analysis results,the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods.At the meantime,it also keeps high stability as the other nonparametric spectrum estimation methods.At last,applications to synthetic waveforms modeled using finite difference method and real data show its efficiency.The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave;and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.展开更多
In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum like...In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.展开更多
Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording con...Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording cone bearing (q<sub>c</sub>), sleeve friction (f<sub>c</sub>) and dynamic pore pressure (u) with depth. The measured q<sub>c</sub>, f<sub>s</sub> and u values are utilized to estimate soil type and associated soil properties. A popular method to estimate soil type from CPT measurements is the Soil Behavior Type (SBT) chart. The SBT plots cone resistance vs friction ratio, R<sub>f</sub> [where: R<sub>f</sub> = (f<sub>s</sub>/q<sub>c</sub>)100%]. There are distortions in the CPT measurements which can result in erroneous SBT plots. Cone bearing measurements at a specific depth are blurred or averaged due to q<sub>c</sub> values being strongly influenced by soils within 10 to 30 cone diameters from the cone tip. The q<sub>c</sub>HMM algorithm was developed to address the q<sub>c</sub> blurring/averaging limitation. This paper describes the distortions which occur when obtaining sleeve friction measurements which can in association with q<sub>c</sub> blurring result in significant errors in the calculated R<sub>f</sub> values. This paper outlines a novel and highly effective algorithm for obtaining accurate sleeve friction and friction ratio estimates. The f<sub>c</sub> optimal filter estimation technique is referred to as the OSFE-IFM algorithm. The mathematical details of the OSFE-IFM algorithm are outlined in this paper along with the results from a challenging test bed simulation. The test bed simulation demonstrates that the OSFE-IFM algorithm derives accurate estimates of sleeve friction from measured values. Optimal estimates of cone bearing and sleeve friction result in accurate R<sub>f</sub> values and subsequent accurate estimates of soil behavior type.展开更多
文摘In this paper, we use Monte Carlo simulations to compare parametric estimators of Type 1 Tobit model. In particular, we examine the performance for finite samples of three different estimators of simple Tobit model: the least squares (LS) estimator, the Heckman (H) estimator and the maximum likelihood (ML) estimator. These three estimators are consistent and asymptotically normal in the case where the density error is specified. However, these properties are sensitive to the situation where the error distribution is not specified. The purpose of this article is to determine properties of the three estimators, namely bias and convergence, by using Monte Carlo simulations.
文摘In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.
文摘This paper is an extension of Hanif, Hamad and Shahbaz estimator [1] for two-phase sampling. The aim of this paper is to develop a regression type estimator with two auxiliary variables for two-phase sampling when we don’t have any type of information about auxiliary variables at population level. To avoid multi-collinearity, it is assumed that both auxiliary variables have minimum correlation. Mean square error and bias of proposed estimator in two-phase sampling is derived. Mean square error of proposed estimator shows an improvement over other well known estimators under the same case.
文摘The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.
文摘AGB (aboveground fresh biomass) is one of the most important parameters of the crop condition monitored with remote sensing. Hyper spectrum remote sensing with the fine spectrum information becomes the efficient method estimating the vegetation AGB. The research was conducted in Xinjiang, the largest cotton planting region of China. The paper analyzed the correlation between the cotton AGB and reflective spectrum and the first derivative spectrum, and the variation coefficient of the waveband reflectance. According to the analysis above, all of 23 parameters, including the hyper spectrum reflectance, the first derivative spectrum parameters and normalization vegetation indexes, were established. And then the estimation models on cotton AGB of relaxing and compact canopy type were established and tested respectively. The tested results showed that Fgo1, [901,502], [901,629], [901,672] among the reflective spectral parameters and D525, D956, D1019, D1751 among the first derivative spectral parameters had the homogenous effect on different cotton canopy types, and the determination coefficients of the models above all arrive at the significant level of 0.99 confidence interval. At last, the tested results of the homogeneity models for different canopy types indicated the parameters of [901, 502], [901,629], [901,672] have more satisfying veracity than others, and the relative errors are as low as 17.0, 16.3 and 16.7% correspondingly; in contrast, the estimation veracity of the first derivative spectrum parameters of single waveband is low.
基金supported by Guangdong Natural Science Foundation(2018A030313508)Science and Technology Program of Guangzhou,China(201804010171)
文摘In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.
基金the National Natural Science Foundation of China (60902054)China Postdoctora Science Foundation (201003758, 20090460114) "Taishan Scholars" Special Foundation of Shandong Province for the support
文摘Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial frequency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively; and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].
文摘Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.
文摘This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.
文摘This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown parameters under a squared error loss function. The approximate Bayes estimators will be computed using the idea of Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions. Also the point estimation and confidence intervals based on maximum likelihood and bootstrap technique are also proposed. The approximate Bayes estimators will be obtained under the assumptions of informative and non-informative priors are compared with the maximum likelihood estimators. A numerical example is provided to illustrate the proposed estimation methods here. Maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo Simulation
文摘Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme. Bayes estimators have been developed using the standard Bayes and MCMC methods under square error and LINEX loss functions, using informative type of priors for the parameters. Simulation comparison of various estimation methods is made when n = 20, 40, 60 and censored data. The Bayes estimates are found to be, generally, better than the maximum likelihood estimates against the proposed prior, in the sense of having smaller mean square errors. This is found to be true whether the data are complete or censored. Estimates improve by increasing sample size. Analysis is also carried out for real life data.
文摘The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.
文摘For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2),Weak L^1(R^2).This extends the theorem of Stein & Wainger and the theo- rem of Weinberg.
文摘In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters. Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators. Numerical examples using real data set are presented to illustrate the methods of inference developed here. Finally, the maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo simulation study.
基金partially supported by the Yangfan project from Guangdong ProvinceNSFC(11571215)
文摘In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.
基金This research was supported by the National Natural Science Foundation of China(No.42274141)Science Foundation of China University of Petroleum,Beijing(No.2462020YXZZ007).
文摘Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient.By designing an appropriate vector filter,phase velocity,attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array.Performance analysis of this algorithm is compared with Extended Prony Method(EPM)and Forward and Backward Matrix Pencil(FBMP)method.Based on the analysis results,the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods.At the meantime,it also keeps high stability as the other nonparametric spectrum estimation methods.At last,applications to synthetic waveforms modeled using finite difference method and real data show its efficiency.The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave;and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.
文摘In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.
文摘Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording cone bearing (q<sub>c</sub>), sleeve friction (f<sub>c</sub>) and dynamic pore pressure (u) with depth. The measured q<sub>c</sub>, f<sub>s</sub> and u values are utilized to estimate soil type and associated soil properties. A popular method to estimate soil type from CPT measurements is the Soil Behavior Type (SBT) chart. The SBT plots cone resistance vs friction ratio, R<sub>f</sub> [where: R<sub>f</sub> = (f<sub>s</sub>/q<sub>c</sub>)100%]. There are distortions in the CPT measurements which can result in erroneous SBT plots. Cone bearing measurements at a specific depth are blurred or averaged due to q<sub>c</sub> values being strongly influenced by soils within 10 to 30 cone diameters from the cone tip. The q<sub>c</sub>HMM algorithm was developed to address the q<sub>c</sub> blurring/averaging limitation. This paper describes the distortions which occur when obtaining sleeve friction measurements which can in association with q<sub>c</sub> blurring result in significant errors in the calculated R<sub>f</sub> values. This paper outlines a novel and highly effective algorithm for obtaining accurate sleeve friction and friction ratio estimates. The f<sub>c</sub> optimal filter estimation technique is referred to as the OSFE-IFM algorithm. The mathematical details of the OSFE-IFM algorithm are outlined in this paper along with the results from a challenging test bed simulation. The test bed simulation demonstrates that the OSFE-IFM algorithm derives accurate estimates of sleeve friction from measured values. Optimal estimates of cone bearing and sleeve friction result in accurate R<sub>f</sub> values and subsequent accurate estimates of soil behavior type.