几类线性模型中的Bootstrap方法及其应用

发布时间：2018-07-04 14:14

本文选题：Behrens-Fisher问题 + Bootstrap重抽样　；参考：《北方工业大学》2015年硕士论文

【摘要】：本文研究了几类线性模型当中的假设检验问题,主要包括均值相等性检验和线性回归模型中参数显著性检验。首先研究了两个正态总体在总体方差未知时的均值检验问题,即Behrens-Fisher问题；然后在此基础上加以推广,考虑了多个总体的在方差未知且不等的情况下的均值检验问题；最后提出一种多元线性模型的参数检验方法,即CAPM的有效性检验,尤其是在样本维度大于样本期数的情况下给出一种新的参数bootstrap检验方法。本文分别提出了三种bootstrap检验方法解决上述三类线性模型的检验问题,首先将bootstrap方法与得分检验结合,给出一种解决Behrens-Fisher问题的方法,其次基于极大似然估计的思想,给出解决多个未知异方差总体的均值检验方法,最后在二次型检验统计量的基础上提出参数bootstrap检验方法。通过Monte Carlo模拟,在解决Behrens-Fisher问题和多正态总体的异方差均值检验问题中,所提出的参数bootstrap检验在控制第一类错误和检验势函数两方面都要优于传统的t检验和广义F检验,而且在样本量较小的情况下,检验效果均令人满意。针对CAPM高维情形下的有效性检验,本文结合广义加号逆的性质提出一种参数bootstrap检验方法,该方法可以用于样本维度大于样本期数的情况,应用范围更加广泛。此外模拟结果表明,已有的针对高维检验方法受随机误差项的非对角元素的显著不为零的影响较大,在弱相关或不相关的情况下效果令人满意,但是在出现强相关时检验犯第一类错误概率相应变大,而提出的参数bootstrap检验可以很好地适应不同强度的相关性要求,检验的精确度更高。
[Abstract]:In this paper, we study the hypothesis testing problems in several linear models, including mean equality test and parameter significance test in linear regression model. The Behrens-Fisher problem, which is the mean test problem of two normal populations with unknown population variance, is studied firstly, and then the mean test problem of multiple populations with unknown and unequal variances is considered based on the generalized Behrens-Fisher problem. Finally, a parameter test method for multivariate linear model is proposed, that is, the validity test of bootstrap, especially when the sample dimension is larger than the sample period, a new parameter bootstrap test method is presented. In this paper, three kinds of bootstrap test methods are proposed to solve the above three kinds of linear models. Firstly, a new method of solving Behrens-Fisher problem is presented by combining bootstrap method with score test, and then based on the idea of maximum likelihood estimation (MLE), a new method is proposed to solve the Behrens-Fisher problem. The mean test method for solving multiple unknown heteroscedasticity populations is given. Finally, a parameter bootstrap test method is proposed on the basis of quadratic type test statistics. By Monte Carlo simulation, in solving the Behrens-Fisher problem and the heteroscedasticity mean test problem of multi-normal population, the proposed parameter bootstrap test is superior to the traditional t test and the generalized F test in controlling the first type error and the test potential function. And in the case of small sample size, the test results are satisfactory. In this paper, we propose a parameter bootstrap test method based on the properties of generalized plus sign inverse, which can be applied to the case where the sample dimension is larger than the number of sample periods, and the scope of application is more extensive. In addition, the simulation results show that the existing methods for high-dimensional test are greatly affected by the significant non-zero of the non-diagonal elements of the random error term, and the results are satisfactory in the case of weak correlation or non-correlation. However, when strong correlation occurs, the probability of the first kind of error becomes larger, and the proposed parameter bootstrap test can well adapt to the correlation requirements of different strength, and the accuracy of the test is higher.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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