This paper considers statistical inference for semiparametric varying coefficient partially linear models with error-prone linear covariates. An empirical likelihood based statistic for parametric component is developed to construct confidence regions. The resulting statistic is shown to be asymptotically chi-square distributed. By the empirical likelihood ratio function, the maximum empirical likelihood estimator of the parameter is defined and the asymptotic normality is shown. A simulation experiment is conducted to compare the empirical likelihood, normal based and the naive empirical likelihood methods in terms of coverage accuracies of confidence regions.

In this article, a procedure for estimating the coefficient functions on the functional-coeffcient regression models with different smoothing variables in different coefficient, functions is defined. Firs step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.

The adaptive varying-coefficient partially linear regression (AVCPLR) model is proposed by combining the nonparametric regression model and varying-coefficient regression model with different smoothing variables. It can be seen as a generalization of the varying-coefficient partially linear regression model, and it is also an example of a generalized structured model as defined by Mammen and Neilsen [Mammen, E., Nielsen, J.P., 2003. Generalised structured models. Biometrika 90, 551 566]. Based on the local linear technique and the marginal integrated method, the initial estimators of these unknown functions are obtained, each of which has big variance. To decrease the variances of these initial estimators, the one-step backfitting technique proposed by Linton [Linton, O.B., 1997. Efficient estimation of additive nonparametric regression models. Biometrika 82, 93 100] is used to obtain the efficient estimators of all unknown functions for the AVCPLR model, and their asymptotic normalities are studied. Two simulated examples are given to illustrate the AVCPLR model and the proposed estimation methodology.

The functional-coefficient regression models with different smoothing variables in different coefficient functions are discussed in this paper. The averaged estimates of coefficient functions are defined by averaging the sample on the initial value obtained by a local linear technique. Their asymptotic normality is studied. The efficiency of the proposed method is shown by a simulated example.

本文给出了样本相互独立，但不同分布的情况下后验概率函数的表达式及其与序贯后验概率函数之间的关系。在此基础上，给出了先验分布和条件分布为0-1分布情况下贝叶斯后验概率大小的比较方法，结合贝叶斯检验分析法安排医疗检查，使其在不降低诊断准确率的前提下，节省检查费用，提出了合理安排医疗检查的建议。