非参数回归模型方差变点的估计

发布时间：2018-02-10 02:37

本文关键词： 方差变点非参数回归变点估计检验统计量　出处：《西安科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：目前时间序列分析中变点问题的研究是统计学研究里一类热门问题,也一直备受国内外众多学者的关注。以往的变点研究主要集中在均值发生变化的情况,如今对方差变点的研究正处在炙热时期。本文首先介绍了变点的相关背景和研究意义,以及非参数回归较参数回归的优势。另外在已有的变点理论和方法的基础上,用非参数方法对两种情形的时间序列方差变点进行了研究。第一种情形是针对独立随机变量单方差变点的研究:针对独立序列均值变点的研究,局部思想法体现出很好的检验估计效果,本文在此基础上用局部思想法和滑窗法的结合对独立随机变量序列中存在方差变点的问题进行研究,并给出了变点的检验统计量和变点的估计,以及检验统计量的极限分布,理论证明了此情形下方差变点估计的强相合性和强收敛速度,并用实验数值模拟验证了此方法的有效性。第二种情形是针对随机设计下非参数回归模型方差变点的研究:利用局部线性核估计来拟合回归曲线,并构造残差序列及CUSUM检验统计量,在一定假设条件下推导证明了检验统计量的渐近分布,验证了检验统计量收敛于Brown桥的上确界,并利用不同的核函数估计验证了局部线性核估计对核函数的选取影响不大,最后用实验数值模拟验证了局部线性核估计较其他核估计存在边界效应的问题明显减弱,这样既改进又拓展了原有的方法。最后对本文做了总结,并提出进一步需要研究的问题。
[Abstract]:At present, the study of change point problem in time series analysis is a kind of popular problem in statistical research, and has been concerned by many scholars both at home and abroad. In the past, the study of change point mainly focused on the change of mean value. At present, the study of the variation point is in a hot period. This paper first introduces the background and significance of the change point, as well as the advantage of non-parametric regression over parametric regression. In addition, on the basis of the existing theory and method of change point, The nonparametric method is used to study the variance variability of time series in two cases. The first case is the single variance change point of independent random variable, the other is the change point of the mean value of independent sequence. The local thought method shows a good effect of test estimation. Based on this, the problem of variance variation point in independent random variable sequence is studied by the combination of local thinking method and sliding window method. The test statistics, the estimates of the change points and the limit distribution of the test statistics are given. The strong consistency and the strong convergence rate of the variance change point estimators are proved theoretically. The effectiveness of the method is verified by experimental numerical simulation. The second case is the study of variance change point of nonparametric regression model under random design: local linear kernel estimation is used to fit the regression curve. The asymptotic distribution of test statistics is proved under certain assumptions, and the convergence of test statistics to the upper bound of Brown bridge is verified. The local linear kernel estimation has little effect on the selection of kernel function by using different kernel function estimators. Finally, the problem of boundary effect between local linear kernel estimators and other kernel estimators is obviously weakened by experimental numerical simulation. This not only improves the original method, but also extends the original method. Finally, the paper summarizes the paper and puts forward some problems that need further study.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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