The probability distributions of wind speeds and the availability of wind turbines were investigated by considering the vertical wind shear. Based on the wind speed data at the standard height observed at a wind farm,...The probability distributions of wind speeds and the availability of wind turbines were investigated by considering the vertical wind shear. Based on the wind speed data at the standard height observed at a wind farm, the power-law process was used to simulate the wind speeds at a hub height of 60 m. The Weibull and Rayleigh distributions were chosen to express the wind speeds at two different heights. The parameters in the model were estimated via the least square(LS) method and the maximum likelihood estimation(MLE) method, respectively. An adjusted MLE approach was also presented for parameter estimation. The main indices of wind energy characteristics were calculated based on observational wind speed data. A case study based on the data of Hexi area, Gansu Province of China was given. The results show that MLE method generally outperforms LS method for parameter estimation, and Weibull distribution is more appropriate to describe the wind speed at the hub height.展开更多
The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0...The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.展开更多
The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and lea...The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.展开更多
In granule processing industries, acquisition of particle size and shape parameters is a common procedure, and volumetric measurement is of great importance in dealing with particle sizing and gradation. To eradicate ...In granule processing industries, acquisition of particle size and shape parameters is a common procedure, and volumetric measurement is of great importance in dealing with particle sizing and gradation. To eradicate the major drawbacks with manual gauge, this paper proposes an optical approach using Back Propagation （BP） neural network to estimate the particle volume based on the two-Dimensional （2D） image information. To achieve the better network efficiency and structure simplicity, Principal Component Analysis （PCA） is adopted to reduce the dimensions of network inputs To overcome the shortcomings of generic BP network for being slow to converge and vulnerable to being trapped in local minimum, Levenberg-Marquardt （LM） algorithm is applied to achieve a higher speed and a lower error rate. The real particle data is utilized in training and testing the presented network. The experimental result suggests that the proposed neural network is capable of estimating aggregate volume with satisfactory precision and superior to the generic BP network in terms of perforxnance capacity.展开更多
The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogene...The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.展开更多
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is c...We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.展开更多
We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regul...We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o（√n）, where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.展开更多
This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which make...This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.60573091 (国家自然科学基金) the National High-Tech Research and Development Plan of China under Grant No.2007AA01Z155 (国家高技术研究发展计划(863))+1 种基金the Program for New Century Excellent Talents in University of China (新世纪优秀人才支持计划)the Beijing Natural Science Foundation of China under Grant No.4073035 (北京市自然科学基金)
基金Project(51165019)supported by the National Natural Science Foundation of ChinaProject(1308RJYA018)supported by Gansu Provincial Natural Science Fund,ChinaProject(2013-4-110)supported by Lanzhou Technology Development Program,China
文摘The probability distributions of wind speeds and the availability of wind turbines were investigated by considering the vertical wind shear. Based on the wind speed data at the standard height observed at a wind farm, the power-law process was used to simulate the wind speeds at a hub height of 60 m. The Weibull and Rayleigh distributions were chosen to express the wind speeds at two different heights. The parameters in the model were estimated via the least square(LS) method and the maximum likelihood estimation(MLE) method, respectively. An adjusted MLE approach was also presented for parameter estimation. The main indices of wind energy characteristics were calculated based on observational wind speed data. A case study based on the data of Hexi area, Gansu Province of China was given. The results show that MLE method generally outperforms LS method for parameter estimation, and Weibull distribution is more appropriate to describe the wind speed at the hub height.
文摘The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.
基金Project(71371182) supported by the National Natural Science Foundation of China
文摘The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.
基金Supported by Ningbo Natural Science Foundation (No. 2006A610016)Foundation of Ministry of Education for Returned Overseas Students & Scholars (SRF for ROCS, SEM. No. 2006699)
文摘In granule processing industries, acquisition of particle size and shape parameters is a common procedure, and volumetric measurement is of great importance in dealing with particle sizing and gradation. To eradicate the major drawbacks with manual gauge, this paper proposes an optical approach using Back Propagation （BP） neural network to estimate the particle volume based on the two-Dimensional （2D） image information. To achieve the better network efficiency and structure simplicity, Principal Component Analysis （PCA） is adopted to reduce the dimensions of network inputs To overcome the shortcomings of generic BP network for being slow to converge and vulnerable to being trapped in local minimum, Levenberg-Marquardt （LM） algorithm is applied to achieve a higher speed and a lower error rate. The real particle data is utilized in training and testing the presented network. The experimental result suggests that the proposed neural network is capable of estimating aggregate volume with satisfactory precision and superior to the generic BP network in terms of perforxnance capacity.
文摘The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.
基金supported by National Natural Science Foundation of China(Grant Nos.1136103011271049 and 11271049)+5 种基金the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry(Grant Nos.CUHK400412HKBU502814211911and 12302714)Hong Kong Research Grants Council(Grant No.Ao E/M-05/12)FRGs of Hong Kong Baptist University
文摘We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.
基金supported by National Institute on Drug Abuse(Grant Nos.R21-DA024260 and P50-DA10075)National Natural Science Foundation of China(Grant Nos.11071077,11371236,11028103,11071022 and 11028103)+2 种基金Innovation Program of Shanghai Municipal Education CommissionPujiang Project of Science and Technology Commission of Shanghai Municipality(Grant No.12PJ1403200)Program for New Century Excellent Talents,Ministry of Education of China(Grant No.NCET-12-0901)
文摘We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o（√n）, where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.
基金supported by the National Natural Science Foundation of China under Grant No.61070236
文摘This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.
