基于平稳遍历函数型非参数递归M估计

发布时间：2018-02-23 02:27

本文关键词： M估计遍历数据几乎完全收敛渐近正态性收敛速度　出处：《合肥工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：作为统计中热门的领域,非参数估计常常面临异常值存在或者残差重尾分布的情况。因此,能减弱估计值不够稳健的M估计方法具有着重要的研究意义,其相关结果也备受学者们的关注。实际研究中数据独立的情况很少,尽管?-混合是常见的混合条件中最弱的,然而要验证非线性时间序列是否符合?-混合条件却很有难度。因此,研究不需要许多条件验证且能包含?-混合不能全部包含的相依结构的遍历性数据是很有必要的。近年来,一些学者建立了改良的M估计方法,目的是在M估计原有的优势上吸收其他估计量的长处。本文采用递归的M估计方法,研究了平稳遍历条件下函数型数据非参数稳健估计的收敛速度以及渐近性质。主要内容如下:1.给出平稳遍历函数型非参数递归M估计的收敛速度:基于平稳遍历函数型数据,构造函数型非参数回归函数的递归M估计量,利用一些合理的正则条件证明非参数递归M回归估计的几乎完全一致收敛并给出收敛速度。推广了现有文献中的相关的结果。2.给出平稳遍历函数型非参数M估计/递归M估计的渐近分布:基于平稳遍历函数型数据,分别给出不同的正则条件,通过合理的推导证明非参数M回归估计的渐近正态性和非参数递归M回归估计的渐近正态性。推广了现有文献中的相关结果。
[Abstract]:As a popular field in statistics, nonparametric estimation is often faced with the existence of outliers or the residual heavy-tailed distribution. Therefore, it is of great significance to study the M estimation method, which can weaken the estimation value and is not robust enough. The related results have attracted the attention of scholars. There are few cases of data independence in practical research, although? -mixing is the weakest of the common mixing conditions, however, to verify whether nonlinear time series match? -mixing conditions are difficult. Therefore, the study does not require a lot of conditional verification and can include? -it is necessary to mix ergodicity data of dependent structures which can not be completely contained. In recent years, some scholars have established an improved M-estimation method. The purpose of this paper is to absorb the advantages of other estimators on the advantage of M estimation. The convergence rate and asymptotic property of nonparametric robust estimation of functional data under stationary ergodic condition are studied. The main contents are as follows: 1. The convergence rate of nonparametric recursive M estimator of stationary ergodic function type is given: based on stationary ergodic function data, Recursive M estimators of nonparametric regression functions of constructor type, Using some reasonable regular conditions, the almost uniform convergence of nonparametric recurrent M regression estimation is proved and the convergence rate is given. The related results. 2. The nonparametric M estimator of stationary ergodic function is given. Asymptotic distribution of / recursive M estimator: based on stationary ergodic function data, The asymptotic normality of nonparametric M regression estimation and the asymptotic normality of nonparametric recurrent M regression estimation are proved by reasonable derivation of different regular conditions.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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