对于递归密度估计的中偏差和大偏差
发布时间：2018-09-17 19:31
【摘要】：本文研究关于密度估计的知识,常见的估计有Rosenblatt估计.Wolverton-Wagner估计和Wegman-Davies估计.主要研究内容是Wegman-Davies估计的中偏差和大偏差.第一章,给出引言,在本章中,主要介绍了研究背景和前人的一些研究成果.其次.提出了我们的研究方向及研究问题.第二章,是本文中重要的部分.在这部分中,介绍了我们的主要研究成果.首先.给出了 Wegman-Davies估计,运用Gartner-Ellis定理对Wegmau-Davies估计进行证明.验证它的中偏差是否成立,若是有偏估计,要加系数对其修正为无偏估计.第三章,我们主要介绍Wegman-Davies递归密度估计的大偏差原理,弱化条件并得到相同,乃至更优化的结论,并且利用概率论的知识用分块证明的方法证明原有结论和新结论.
[Abstract]:In this paper, we study the knowledge of density estimation. The common estimators are Rosenblatt estimators. Wolverton-Wagner estimators and Wegman-Davies estimators. The main content of this paper is the medium deviation and large deviation of Wegman-Davies estimation. In the first chapter, the introduction is given. In this chapter, the research background and some previous research results are introduced. Secondly. The research direction and problems are put forward. The second chapter is the important part of this paper. In this part, we introduce our main research results. First The Wegman-Davies estimate is given, and the Wegmau-Davies estimate is proved by Gartner-Ellis theorem. It is verified that the intermediate deviation is true. If there is a biased estimate, the additive coefficient should be modified to the unbiased estimate. In the third chapter, we mainly introduce the large deviation principle of Wegman-Davies recursive density estimation, the weakening condition and get the same, even more optimized conclusion, and use the knowledge of probability theory to prove the original conclusion and the new conclusion by using the method of block proof.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2246876
[Abstract]:In this paper, we study the knowledge of density estimation. The common estimators are Rosenblatt estimators. Wolverton-Wagner estimators and Wegman-Davies estimators. The main content of this paper is the medium deviation and large deviation of Wegman-Davies estimation. In the first chapter, the introduction is given. In this chapter, the research background and some previous research results are introduced. Secondly. The research direction and problems are put forward. The second chapter is the important part of this paper. In this part, we introduce our main research results. First The Wegman-Davies estimate is given, and the Wegmau-Davies estimate is proved by Gartner-Ellis theorem. It is verified that the intermediate deviation is true. If there is a biased estimate, the additive coefficient should be modified to the unbiased estimate. In the third chapter, we mainly introduce the large deviation principle of Wegman-Davies recursive density estimation, the weakening condition and get the same, even more optimized conclusion, and use the knowledge of probability theory to prove the original conclusion and the new conclusion by using the method of block proof.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
【参考文献】
相关期刊论文 前2条
1 张冬霞;梁汉营;;样本的递归密度估计(英文)[J];应用概率统计;2008年02期
2 韦来生;NA样本概率密度函数核估计的相合性[J];系统科学与数学;2001年01期
，本文编号：2246876
本文链接：https://www.wllwen.com/kejilunwen/yysx/2246876.html
