Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than convention...This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.展开更多
In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many d...In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber's estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.展开更多
The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that th...The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that the M-estimators of the vector of parameters are asymptotically normal and the M-estimators of the nonparametric component achieve the optimal convergence rates for nonparametric regression. Our asymptotic theory includes L1-, L2-, Lp-norm, and Huber estimators as special cases.展开更多
Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O(...Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O(|n|^-1/5), n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(|n|^-4/5 log |n|). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.展开更多
This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. ...This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A (FY-3A) simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.展开更多
In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct ...Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.展开更多
Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MS...Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.展开更多
Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes...Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for estimating the coefficient functions and develop a robustified generalized likelihood ratio (GLR) statistic to test if some of the coefficient functions are constants or of certain parametric forms. The robustified GLR test is robust against outliers and the error distribution. This provides a useful robust inference tool for the models with longitudinal data. The bandwidth selection issue is also addressed to facilitate the implementation in practice. Simulations show that the proposed testing method is more powerful in some situations than its counterpart based on the least squares principle. A real example is also given for illustration.展开更多
In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator...In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.展开更多
The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptica...The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.展开更多
Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based appr...Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based approaches. This paper explores a different approach of nonlocal-means filter by using robust M-estimator function rather than the exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels with surrounding neighborhoods using the chosen robust M-estimator function. The main direction of this paper is to identify the best robust M-estimator function for nonlocal-means denoising algorithm. In order to speed up the computation, a new patch classification method is followed to eliminate the uncorrelated patches from the weighted averaging process. This patch classification approach compares favorably to existing techniques in respect of quality versus computational time. Validations using standard test images and brain atlas images have been analyzed and the results were compared with the other known methods. It is seen that there is reason to believe that the proposed refined technique has some notable points.展开更多
The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under ...The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.展开更多
A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of r...A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M- estimators and makes them possible to cope well with spatially inho-mogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative展开更多
The strong consistency of M-estimates of the regression coefficients in a linear modelunder some mild conditions is established, which is an essential improvement over the relevantresults in the literature on the mome...The strong consistency of M-estimates of the regression coefficients in a linear modelunder some mild conditions is established, which is an essential improvement over the relevantresults in the literature on the moment condition. Especially, in some important circumstances, onlyE ψ(ek) q for some q>1 is needed, where ψ(eκ) is some score function of random error.展开更多
In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute...In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute,an up-dating recursion procedure is proposed to simplify the com-putation of the estimators when a new observation is obtained.We show that,under mild conditions,the recursion estimates are strongly consistent.In addition,the asymptotic normality of the recursive constrained M-estimators of regression coeffcients is established.A Monte Carlo simulation study of the recursion estimates is also provided.Besides,robustness and asymptotic behavior of constrained M-estimators are briefly discussed.展开更多
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金the National Natural Science Foundation of China (Nos. 60172071 and 60372005)
文摘This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871153 and 10971047)
文摘In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber's estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.
基金Project supported in part by the Postdoctoral Science Foundation and the National Natural Science Foundation of China.
文摘The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that the M-estimators of the vector of parameters are asymptotically normal and the M-estimators of the nonparametric component achieve the optimal convergence rates for nonparametric regression. Our asymptotic theory includes L1-, L2-, Lp-norm, and Huber estimators as special cases.
基金National Natural Science Foundation of China (No.10771192)
文摘Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O(|n|^-1/5), n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(|n|^-4/5 log |n|). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.
基金Supported by Special Scientific Research Fund of Meteorological Public Welfare Profession of China(GYHY201406028)Meteorological Open Research Fund for Huaihe River Basin(HRM201407)Anhui Meteorological Bureau Science and Technology Development Fund(RC201506)
文摘This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A (FY-3A) simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.
文摘In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
文摘Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.
文摘Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.
文摘Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for estimating the coefficient functions and develop a robustified generalized likelihood ratio (GLR) statistic to test if some of the coefficient functions are constants or of certain parametric forms. The robustified GLR test is robust against outliers and the error distribution. This provides a useful robust inference tool for the models with longitudinal data. The bandwidth selection issue is also addressed to facilitate the implementation in practice. Simulations show that the proposed testing method is more powerful in some situations than its counterpart based on the least squares principle. A real example is also given for illustration.
基金This work is supported by the Universiti Kebangsaan Malaysia[Grant Number DIP-2018-038].
文摘In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.
文摘The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.
文摘Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based approaches. This paper explores a different approach of nonlocal-means filter by using robust M-estimator function rather than the exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels with surrounding neighborhoods using the chosen robust M-estimator function. The main direction of this paper is to identify the best robust M-estimator function for nonlocal-means denoising algorithm. In order to speed up the computation, a new patch classification method is followed to eliminate the uncorrelated patches from the weighted averaging process. This patch classification approach compares favorably to existing techniques in respect of quality versus computational time. Validations using standard test images and brain atlas images have been analyzed and the results were compared with the other known methods. It is seen that there is reason to believe that the proposed refined technique has some notable points.
文摘The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.
文摘A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M- estimators and makes them possible to cope well with spatially inho-mogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10171094), and Ph. D. Program Foundation of the Ministry of Education of China (Grant No. 2000035803).
文摘The strong consistency of M-estimates of the regression coefficients in a linear modelunder some mild conditions is established, which is an essential improvement over the relevantresults in the literature on the moment condition. Especially, in some important circumstances, onlyE ψ(ek) q for some q>1 is needed, where ψ(eκ) is some score function of random error.
基金supported by the Natural Sciences and Engineering Research Council of Canada
文摘In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute,an up-dating recursion procedure is proposed to simplify the com-putation of the estimators when a new observation is obtained.We show that,under mild conditions,the recursion estimates are strongly consistent.In addition,the asymptotic normality of the recursive constrained M-estimators of regression coeffcients is established.A Monte Carlo simulation study of the recursion estimates is also provided.Besides,robustness and asymptotic behavior of constrained M-estimators are briefly discussed.