面板计数数据的统计推断

发布时间：2018-03-22 09:04

本文选题：面板计数数据　切入点：复发事件　出处：《吉林大学》2016年博士论文　论文类型：学位论文

【摘要】：面板计数数据在近年来引起了统计学者的广泛关注,这类数据经常出现在医学,经济学,人口学,社会学等研究领域中.本文主要研究了面板计数数据的假设检验与回归分析问题.首先,我们研究了具有不相同观测过程的面板计数数据的假设检验问题,我们提出了一类新的假设检验方法,并证明了检验统计量的渐近正态性.其次,我们考虑了面板计数数据与区间删失数据的联合回归分析问题,这里我们使用Sieve极大似然估计方法给出了回归参数的估计,并通过利用Bernstein多项式逼近未知函数的办法来简化问题.此时得到的估计量具有相合性与渐近正态性.最后我们考虑了在加性均值模型下,当协变量带有测量误差时,面板计数数据的回归分析问题.我们利用估计方程与SIMEX方法给出了回归参数的估计,并证明了所得到的SIMEX估计的渐近正态性.
[Abstract]:Panel count data have attracted the attention of statisticians in recent years, such data often appear in medicine, economics, demography, In sociology and other research fields, this paper mainly studies the hypothesis test and regression analysis of panel count data. Firstly, we study the hypothesis test problem of panel count data with different observation process. We propose a new hypothesis test method, and prove the asymptotic normality of test statistics. Secondly, we consider the joint regression analysis of panel count data and interval censored data. Here we use the Sieve maximum likelihood estimation method to estimate the regression parameters. The problem is simplified by using Bernstein polynomials to approximate unknown functions. The obtained estimators are consistent and asymptotically normal. Finally, we consider the covariables with measurement errors in the additive mean model. In this paper, we use the estimation equation and SIMEX method to estimate the regression parameters, and prove the asymptotic normality of the obtained SIMEX estimators.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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