Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades...Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.展开更多
Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of ...Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.展开更多
Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcom...Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.展开更多
Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and varianc...Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.展开更多
Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and(or) the variance model, and cannot be used to select the joint mean, va...Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and(or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes,and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.展开更多
Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has rece...Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.展开更多
Many products always operate under various complex environment conditions. To describe the dynamic influence of environment factors on their reliability, a method of reliability sensitivity analysis is proposed. In th...Many products always operate under various complex environment conditions. To describe the dynamic influence of environment factors on their reliability, a method of reliability sensitivity analysis is proposed. In this method, the location parameter is assumed as a function of relevant environment variables while the scale parameter is assumed as an unknown positive constant. Then, the location parameter function is constructed by using the method of radial basis function. Using the varied environment test data, the log-likelihood function is transformed to a generalized linear expression by describing the indicator as Poisson variable. With the generalized linear model, the maximum likelihood estimations of the model coefficients are obtained. With the reliability model, the reliability sensitivity is obtained. An instance analysis shows that the method is feasible to analyze the dynamic variety characters of reliability along with environment factors and is straightforward for engineering application.展开更多
基金Supported by the National Natural Science Foundation of China(11261025,11561075)the Natural Science Foundation of Yunnan Province(2016FB005)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.
基金Supported by the National Natural Science Foundation of China(11861041).
文摘Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.
基金Supported by the National Natural Science Foundation of China(11261025,11201412)the Natural Science Foundation of Yunnan Province(2011FB016)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.
文摘Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.
基金supported by the National Natural Science Foundation of China under Grant Nos.11261025,11561075the Natural Science Foundation of Yunnan Province under Grant No.2016FB005the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and(or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes,and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.
文摘Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.
文摘Many products always operate under various complex environment conditions. To describe the dynamic influence of environment factors on their reliability, a method of reliability sensitivity analysis is proposed. In this method, the location parameter is assumed as a function of relevant environment variables while the scale parameter is assumed as an unknown positive constant. Then, the location parameter function is constructed by using the method of radial basis function. Using the varied environment test data, the log-likelihood function is transformed to a generalized linear expression by describing the indicator as Poisson variable. With the generalized linear model, the maximum likelihood estimations of the model coefficients are obtained. With the reliability model, the reliability sensitivity is obtained. An instance analysis shows that the method is feasible to analyze the dynamic variety characters of reliability along with environment factors and is straightforward for engineering application.
