【摘要】：本文研究關(guān)于密度估計(jì)的知識(shí),常見(jiàn)的估計(jì)有Rosenblatt估計(jì).Wolverton-Wagner估計(jì)和Wegman-Davies估計(jì).主要研究?jī)?nèi)容是Wegman-Davies估計(jì)的中偏差和大偏差.第一章,給出引言,在本章中,主要介紹了研究背景和前人的一些研究成果.其次.提出了我們的研究方向及研究問(wèn)題.第二章,是本文中重要的部分.在這部分中,介紹了我們的主要研究成果.首先.給出了 Wegman-Davies估計(jì),運(yùn)用Gartner-Ellis定理對(duì)Wegmau-Davies估計(jì)進(jìn)行證明.驗(yàn)證它的中偏差是否成立,若是有偏估計(jì),要加系數(shù)對(duì)其修正為無(wú)偏估計(jì).第三章,我們主要介紹Wegman-Davies遞歸密度估計(jì)的大偏差原理,弱化條件并得到相同,乃至更優(yōu)化的結(jié)論,并且利用概率論的知識(shí)用分塊證明的方法證明原有結(jié)論和新結(jié)論.
[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.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

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本文編號(hào)：2246876