关于方差估计和比较的一种半参数方法

发布时间：2018-04-17 07:04

本文选题：半参数密度函数比模型 + 经验似然　；参考：《南京财经大学》2015年硕士论文

【摘要】：对总体的方差进行估计和假设检验是很基本的统计问题.传统的方差估计和假设检验主要集中在参数和非参数的方法上.参数方法有建立在正态假设下关于单个方差的卡方检验和两个方差比较的F检验等.非参数方法则不要求假设总体服从正态分布,从次序统计量或者方差点估计量的渐近分布出发构造统计量进行有关的统计推断,最新的非参数方法是从经验似然的角度构造统计量实现对方差的估计和检验.当总体服从正态假设时非参数方法对于参数方法的渐近相对效率较低,反之则非参数方法更优.针对总体方差的估计和检验,本文提出一种新的方法,在半参数密度函数比模型下对总体方差进行半参数估计,并且构造检验统计量对两总体方差进行假设检验.本文给出了一些理论和统计模拟结果,并在理论基础上进行了实例分析.统计模拟结果显示半参数方法在数据满足正态性假设时,检验效能略好于参数方法和非参数方法；而当数据不再满足正态性假设时,半参数方法具有明显的优势.实例分析中,我们选用了文献中的真实数据对我们提出的半参数方法进行验证,假设检验得出的结论与非参数方法的结论一致.第一章绪论,描述问题提出的背景及意义,概括研究现状,简要介绍相关的预备知识.第二章在半参数密度函数比模型下,首先给出单总体方差的渐近估计,同时在计算证明过于复杂的情况下,提出应用Bootstrap方法对方差进行估计；然后对两总体方差做半参数方法下统计推断,并给出半参数估计量优于非参数估计量的理论结果；最后构建了Wald型检验统计量.第三章统计模拟和实例分析,在数据满足正态假设和不满足正态假设两种情形下,分别给出了两样本F检验、半参数方法检验和非参数方法检验的检验效能；并利用半参数方法对真实样本数据进行估计和检验.第四章对全文进行总结并加以展望.
[Abstract]:It is a basic statistical problem to estimate and test the variance of population.Traditional variance estimation and hypothesis test mainly focus on parametric and non-parametric methods.The parametric methods include chi-square test for single variance and F test for comparison of two variances under normal assumption.The nonparametric method does not require the assumption that the population service is based on the normal distribution, and that the statistics are constructed from the asymptotic distribution of the order statistics or the square handicap estimators.The latest nonparametric method is to construct statistics from the perspective of empirical likelihood to estimate and test the difference.The asymptotic relative efficiency of the nonparametric method is lower than that of the non-parametric method when the population is assumed to be normal. Otherwise, the non-parametric method is better.In this paper, a new method is proposed to estimate the total variance under the semi-parametric density function ratio model, and a test statistic is constructed to test the hypothesis of the two variances.In this paper, some theoretical and statistical simulation results are given, and an example is given on the basis of the theory.The statistical simulation results show that the semi-parametric method has a better performance than the parametric method and the non-parametric method when the data satisfy the normal hypothesis, but the semi-parametric method has obvious advantages when the data no longer satisfies the normality hypothesis.In the case analysis, we use the real data in the literature to verify the semi-parametric method proposed by us, and the hypothesis test results are consistent with the conclusion of the non-parametric method.The first chapter is an introduction, describing the background and significance of the question, summarizing the current situation of the research, and briefly introducing the relevant preparatory knowledge.In the second chapter, under the semi-parametric density function ratio model, the asymptotic estimation of the variance of a single population is first given. At the same time, the Bootstrap method is used to estimate the variance when the calculation proves that the variance is too complicated.Then the statistical inference is made for the two variances under the semi-parametric method, and the theoretical results that the semi-parametric estimator is superior to the non-parametric estimator are given. Finally, the Wald type test statistic is constructed.Chapter 3 is statistical simulation and case analysis. Under the two cases of data satisfying normal hypothesis and not satisfying normal hypothesis, the test effectiveness of two samples F test, half parameter method test and non parameter method test are given respectively.The semi-parametric method is used to estimate and test the real sample data.Chapter four summarizes the full text and looks forward to it.
【学位授予单位】：南京财经大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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