For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be...For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.展开更多
In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properti...In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.展开更多
文摘For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.
基金supported by the National Natural Science Foundation of China(No.12571284,No.12171203)supported by the National Natural Science Foundation of China(No.12561051)+3 种基金the Fundamental Research Funds for the Central Universities(No.23JNQMX21)supported by the University-level scientific research project of Guangdong University of Foreign Studies(NO.299-GK25G301/25TS10)supported by a grant from National Natural Foundation of China(No.12171225)Yunnan Province Xing Dian Talent Support Program(YNWR-YLXZ-2018-020)。
文摘In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.
