本文選題：多小波 + 非參密度估計��； 參考：《北京化工大學(xué)》2015年碩士論文

【摘要】：統(tǒng)計學(xué)中的一個重要問題就是概率密度估計,不管是在理論研究方面還是實際應(yīng)用方面,概率密度估計對于解決統(tǒng)計學(xué)中的大部分問題都有非常重要的幫助。過去用于密度估計的方法主要是直方圖估計和核估計,小波分析的發(fā)展為解決概率密度函數(shù)估計提供了更多的選擇,鑒于小波基存在正交性和良好的局部自適應(yīng)性,這也就讓小波密度函數(shù)估計在處理局部震蕩或者有突變的信號方面相比于傳統(tǒng)的非參數(shù)密度估計有一定的優(yōu)勢。密度估計的小波方法為解決特殊信號的概率密度估計提供了有效的手段,但是由于單小波基不能同時滿足對稱性,正交性和緊支稱性,多小波基能夠同時滿足上述性質(zhì),所以我們選擇多小波基進(jìn)行密度函數(shù)估計。本文在已有的單小波密度函數(shù)估計的基礎(chǔ)上,選擇多小波基進(jìn)行研究,把單小波方法推廣到多小波中。文章首先推導(dǎo)出了多小波密度估計的表示形式,并對線性多小波密度估計進(jìn)行討論;其次對密度函數(shù)的多小波估計的線性情形進(jìn)行穩(wěn)健性分析,得到其收斂階,證明了理論上的可行性;最后選擇實驗數(shù)據(jù)用此方法進(jìn)行估計分析,通過實驗結(jié)論進(jìn)一步論證密度函數(shù)的多小波估計方法的可行性。
[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.
【學(xué)位授予單位】：北京化工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.1

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相關(guān)期刊論文 前3條

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本文編號：1820177