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。

It is well known that the exposure to ambient air pollution might cause serious respiratory illnesses and that the weather conditions may also contribute to the seriousness. However, quantifying the effects of pollution and the weather condition is a difficult task due to the nonlinear nature of these impacts. The problem is further complicated by the possibly cumulative effects of these impacts. In this paper, the nonparametric additive (NPA) models, which have the advantage of ease in interpretation and forecasting, are employed for modeling the effects of pollution and weather. All models are derived by the local linear method. The variables in the final selected NPA model are chosen by cross-validation method together with bootstrap test for the data of Hong Kong. For comparison the final selected linear regression (LR) model by the backward elimination method is also considered. It is found, interestingly, that the variables selected by nonparametric method and the usual backward elimination method for linear models are different. Furthermore, by comparing forecasted values obtained from the NPA and LR models and true values the final selected NPA model is shown to outperform the LR model.

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.

Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.

考虑部分线性单指标模型参数部分的统计推断问题。主要研究利用剖面最小二乘法（profile least-squares technique）估计模型的未知参数和函数，并利用该估计建立模型中参数部分的广义似然比（generalized likelihood ratio, GLR）检验统计量。在原假设条件下，文中新提出的GLR检验统计量渐近服从具有尺度常数（scale constant）与自由度独立于讨厌参数（nuisance parameters）的χ2-分布，这一现象被称为Wilks现象。最后给出数字模拟与实际例子，验证文中所提出的检验方法。