基于多小波的密度估计及其应用研究

发布时间：2018-04-29 13:44

本文选题：多小波 + 非参密度估计　；参考：《北京化工大学》2015年硕士论文

【摘要】：统计学中的一个重要问题就是概率密度估计,不管是在理论研究方面还是实际应用方面,概率密度估计对于解决统计学中的大部分问题都有非常重要的帮助。过去用于密度估计的方法主要是直方图估计和核估计,小波分析的发展为解决概率密度函数估计提供了更多的选择,鉴于小波基存在正交性和良好的局部自适应性,这也就让小波密度函数估计在处理局部震荡或者有突变的信号方面相比于传统的非参数密度估计有一定的优势。密度估计的小波方法为解决特殊信号的概率密度估计提供了有效的手段,但是由于单小波基不能同时满足对称性,正交性和紧支称性,多小波基能够同时满足上述性质,所以我们选择多小波基进行密度函数估计。本文在已有的单小波密度函数估计的基础上,选择多小波基进行研究,把单小波方法推广到多小波中。文章首先推导出了多小波密度估计的表示形式,并对线性多小波密度估计进行讨论;其次对密度函数的多小波估计的线性情形进行稳健性分析,得到其收敛阶,证明了理论上的可行性;最后选择实验数据用此方法进行估计分析,通过实验结论进一步论证密度函数的多小波估计方法的可行性。
[Abstract]:One of the most important problems in statistics is probability density estimation. Whether in theory research or practical application, probability density estimation is very important to solve most of the problems in statistics. In the past, the methods of density estimation were mainly histogram estimation and kernel estimation. The development of wavelet analysis provided more options for solving probability density function estimation. In view of the orthogonality and good local adaptability of wavelet bases, This makes wavelet density function estimation have some advantages over traditional nonparametric density estimation in dealing with local oscillation or sudden signal. The wavelet method of density estimation provides an effective method for solving the probability density estimation of special signals. However, because the single wavelet basis can not satisfy the symmetry, orthogonality and compactness at the same time, the multi-wavelet basis can satisfy the above properties at the same time. So we select multiple wavelet bases to estimate the density function. In this paper, based on the existing density function estimation of single wavelet, the multiwavelet basis is selected to study, and the simple wavelet method is extended to multiwavelet. In this paper, the representation of multiwavelet density estimation is derived, and the linear multiwavelet density estimation is discussed. The feasibility of the method is proved in theory, and the feasibility of the multiwavelet estimation method of density function is further demonstrated by the experimental results.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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