纵向数据下变系数部分线性EV模型的参数估计与模型检验

发布时间：2018-03-14 03:36

本文选题：随机效应　切入点：固定效应　出处：《北京化工大学》2016年硕士论文　论文类型：学位论文

【摘要】：纵向数据是实践分析中一种常见的数据类型,它既含有时间序列数据又包含横截面数据,从而可在研究客观目标的动态行为时提供非常有用的信息。统计分析中针对纵向数据的研究模型和方法有很多,其中变系数部分线性模型因其具有较强的解释能力和灵活性而在统计和经济等领域得到广泛的应用。实际生活中对于数据的采集可能存在各种测量误差,因此基于纵向数据建立变系数部分线性EV模型具有很强的现实意义,并成为统计学界研究的重点课题之一。本文研究了纵向数据下变系数部分线性EV模型的参数估计和个体效应的检验问题。首先在忽略测量误差的情况下,通过最小二乘估计方法和局部线性估计方法,分别在随机效应模型和固定效应模型下导出了参数和非参数部分的估计量。进一步当协变量带有测量误差时,经过纠偏处理得到修正后的估计量,并在大样本下证明估计具有相合性和渐近正态性。为了识别个体效应的类型,我们提出参数Hausman检验统计量对模型个体效应进行检验。我们分别在大样本和小样本下讨论了参数Hausman检验的应用,首先从理论上证明了参数检验统计量在大样本下渐近服从卡方分布,并模拟结果显示参数估计量的估计效果不错且在随机效应假设下检验统计量近似服从卡方分布；而在小样本下结合Bootstrap抽样方法得到检验的拒绝域,并通过模拟研究验证检验统计量的检验功效,数值模拟结果显示基于Bootstrap抽样的参数Hausman检验在小样本下具有很好的表现。
[Abstract]:Longitudinal data is a common data type in practical analysis. It contains both time series data and cross section data. This provides very useful information when studying the dynamic behavior of objective targets. There are many models and methods for longitudinal data in statistical analysis. Among them, partial linear models with variable coefficients have been widely used in statistical and economic fields because of their strong explanatory ability and flexibility. Therefore, it is of great practical significance to establish partial linear EV model with variable coefficients based on longitudinal data. In this paper, the parameter estimation and individual effect test of partial linear EV model with variable coefficients under longitudinal data are studied. By using the least square estimation method and the local linear estimation method, the estimators of the parametric and non-parametric parts are derived under the stochastic effect model and the fixed effect model, respectively. The modified estimator is obtained by rectifying the error, and the consistency and asymptotic normality of the estimator are proved under the large sample. In order to identify the type of individual effect, We propose a parameter Hausman test statistic to test the individual effects of the model. We discuss the application of parametric Hausman test in large and small samples, respectively. Firstly, it is proved theoretically that the parameter test statistics are asymptotically obedient to the chi-square distribution under large samples, and the simulation results show that the estimation effect of the parameter estimators is good and the test statistics are similar to the subordinate chi-square distributions under the assumption of random effects. Under the small sample and Bootstrap sampling method, the test rejection domain is obtained, and the effectiveness of test statistics is verified by simulation research. The numerical simulation results show that the parameter Hausman test based on Bootstrap sampling has a good performance in small samples.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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