Joint Variable Selection of Mean-Covariance Model for Longitudinal Data

In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Partial Functional Linear Models with ARCH Errors

In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.

Variable Selection for Partially Linear Varying Coefficient Transformation Models with Censored Data

In this paper, we study the problem of variable selection for varying coefficient transformation models with censored data. We fit the varying coefficient transformation models by maximizing the marginal likelihood subject to a shrink- age-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. We further provide an efficient computation algorithm to implement the proposed methods. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed as an illustration.

基于众数回归的部分函数型线性可加模型的稳健估计

本文讨论部分函数型线性可加模型参数的稳健估计,该模型由经典的可加回归模型和函数型线性模型组合而成.采用B-样条基函数对模型中斜率函数和非参数可加函数进行近似,然后通过最大化众数回归目标函数得到基于众数回归的估计.在一些正则条件下,本文给出估计的收敛速度和渐近分布.最后通过模拟计算和应用实例以表明所提方法的有效性.模拟结果表明,该方法不仅具有稳健性,即不易受污染数据或厚尾分布的影响,而且在信噪比较大时可以与最小二乘方法有相同的表现.

Statistical inference in the partial functional linear expectile regression model

As extensions of means, expectiles embrace all the distribution information of a random variable.The expectile regression is computationally friendlier because the asymmetric least square loss function is differentiable everywhere. This regression also enables effective estimation of the expectiles of a response variable when potential explanatory variables are given. In this study, we propose the partial functional linear expectile regression model. The slope function and constant coefficients are estimated by using the functional principal component basis. The convergence rate of the slope function and the asymptotic normality of the parameter vector are established. To inspect the effect of the parametric component on the response variable, we develop Wald-type and expectile rank score tests and establish their asymptotic properties. The finite performance of the proposed estimators and test statistics are evaluated through simulation study. Results indicate that the proposed estimators are comparable to competing estimation methods and the newly proposed expectile rank score test is useful. The methodologies are illustrated by using two real data examples.

Randomized statistical inference:A unified statistical inference frame of frequentist,fiducial,and Bayesian inference

We propose randomized inference(RI),a new statistical inference approach.RI may be realized through a randomized estimate(RE)of a parameter vector,which is a random vector that takes values in the parameter space with a probability density function(PDF)that depends on the sample or sufficient statistics,such as the posterior distributions in Bayesian inference.Based on the PDF of an RE of an unknown parameter,we propose a framework for both the vertical density representation(VDR)test and the construction of a confidence region.This approach is explained with the aid of examples.For the equality hypothesis of multiple normal means without the condition of variance homogeneity,we present an exact VDR test,which is shown as an extension of one-way analysis of variance(ANOVA).In the case of two populations,the PDF of the Welch statistics is given by using the RE.Furthermore,through simulations,we show that the empirical distribution function,the approximated t,and the RE distribution function of Welch statistics are almost equal.The VDR test of the homogeneity of variance is shown to be more efficient than both the Bartlett test and the revised Bartlett test.Finally,we discuss the prospects of RI.