The optimally weighted least squares estimate and the linear minimum variance estimateare two of the most popular estimation methods for a linear model.In this paper,the authors makea comprehensive discussion about th...The optimally weighted least squares estimate and the linear minimum variance estimateare two of the most popular estimation methods for a linear model.In this paper,the authors makea comprehensive discussion about the relationship between the two estimates.Firstly,the authorsconsider the classical linear model in which the coefficient matrix of the linear model is deterministic,and the necessary and sufficient condition for equivalence of the two estimates is derived.Moreover,under certain conditions on variance matrix invertibility,the two estimates can be identical providedthat they use the same a priori information of the parameter being estimated.Secondly,the authorsconsider the linear model with random coefficient matrix which is called the extended linear model;under certain conditions on variance matrix invertibility,it is proved that the former outperforms thelatter when using the same a priori information of the parameter.展开更多
We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile m...We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.展开更多
In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property...In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.展开更多
We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We o...We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.展开更多
Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,an...Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.展开更多
In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least ...In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos 60232010, 60574032the Project 863 under Grant No. 2006AA12A104
文摘The optimally weighted least squares estimate and the linear minimum variance estimateare two of the most popular estimation methods for a linear model.In this paper,the authors makea comprehensive discussion about the relationship between the two estimates.Firstly,the authorsconsider the classical linear model in which the coefficient matrix of the linear model is deterministic,and the necessary and sufficient condition for equivalence of the two estimates is derived.Moreover,under certain conditions on variance matrix invertibility,the two estimates can be identical providedthat they use the same a priori information of the parameter being estimated.Secondly,the authorsconsider the linear model with random coefficient matrix which is called the extended linear model;under certain conditions on variance matrix invertibility,it is proved that the former outperforms thelatter when using the same a priori information of the parameter.
文摘We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.
文摘In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.
文摘We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.
基金the National Nature Science Foundation of China under Grant Nos.11571024and 11771032the Humanities and Social Science Foundation of Ministry of Education of China under Grant No.20YJCZH245。
文摘Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.
基金Supported by the Educational Commission of Hubei Province of China(Grant No.D20112503)National Natural Science Foundation of China(Grant Nos.11071022,11231010 and 11028103)the foundation of Beijing Center of Mathematics and Information Sciences
文摘In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.