纵向数据下部分线性单指标模型的若干问题研究

发布时间：2018-12-28 08:43

【摘要】：本文针对纵向数据,研究部分线性单指标模型的稳健估计及其变量选择,研究内容主要有以下几个方面:第一,在纵向数据下,针对部分线性单指标回归模型,基于稳健分位数回归方法,对模型中单指标部分和线性部分都做了分位数处理,采用局部多项式方法估计连接函数,在一定的条件下,证明了所得的估计量具有渐近正态性,给出了估计算法的实施步骤。通过数值模拟分析,比较了不同点分位数回归连接函数的估计效果,验证了所提方法的稳健性和有效性。实例分析Boston房价数据,进一步说明了所提出方法的实际应用价值。第二,基于LASSO、ALASSO双重自适应惩罚估计方法,提出稳健化的似然函数,针对纵向数据,研究单指标线性混合效应模型下,固定效应和随机效应的联合稳健变量选择,采用惩罚样条逼近方法,对单指标部分未知连接函数采取惩罚样条逼近。在一些正则化条件下,证明了惩罚稳健估计的Oracle性质。模拟研究中,比较污染与不污染数据时所提方法的影响,结果表明所提变量选择方法具有稳健性。实例分析一组CD4数据,得到的结果说明所提出方法的有效性和实用性。
[Abstract]:Based on the longitudinal data, the robust estimation and variable selection of partial linear single index model are studied in this paper. The main contents are as follows: first, under the longitudinal data, for partial linear single index regression model, Based on the robust quantile regression method, the quantiles of the single index part and the linear part of the model are processed, and the connection function is estimated by using the local polynomial method. Under certain conditions, the asymptotic normality of the obtained estimator is proved. The implementation steps of the estimation algorithm are given. By numerical simulation, the estimation effect of the regression connection function of different quantiles is compared, and the robustness and validity of the proposed method are verified. An example is given to illustrate the practical application value of the proposed method by analyzing the Boston housing price data. Secondly, based on the LASSO,ALASSO double adaptive penalty estimation method, a robust likelihood function is proposed. For the longitudinal data, the joint robust variable selection of fixed and random effects is studied under the single parameter linear mixed effect model. The penalty spline approximation method is applied to the partial unknown connection function of a single parameter. Under some regularization conditions, the Oracle property of the penalized robust estimate is proved. In the simulation study, the effects of the proposed method on the pollution and non-pollution data are compared. The results show that the proposed method is robust. An example is given to analyze a set of CD4 data, and the results show the effectiveness and practicability of the proposed method.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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