發(fā)布時間：2018-04-29 04:20

  本文選題：異常值 + 回歸分析��； 參考：《蘭州商學(xué)院》2014年碩士論文

【摘要】：回歸分析是一種統(tǒng)計學(xué)上分析數(shù)據(jù)的方法，其目的在于了解兩個或多個變量間是否相關(guān)、相關(guān)方向與強度，并建立數(shù)學(xué)模型以便觀察特定變量來預(yù)測、控制研究者感興趣的變量。經(jīng)典的線性回歸模型理論創(chuàng)立以來，被廣泛應(yīng)用于自然科學(xué)與社會科學(xué)等許多領(lǐng)域中，并取得許多成果。但是應(yīng)用回歸分析的時候經(jīng)常存在異常值，這些異常值會直接影響到我們所做的回歸模型與現(xiàn)實情況是否能很好地擬合、以及參數(shù)估計的精確程度、模型的穩(wěn)定程度等一系列涉及到回歸分析本身的問題。因此，對異常值的診斷和處理是一個兼具理論意義和實際意義的問題。 異常值的診斷方法一直備受學(xué)者們的關(guān)注，但是迄今為止，還沒有一種標準或者廣泛適用的方法。本文對應(yīng)用較為廣泛的兩類診斷異常值的方法——基于LS的和基于穩(wěn)健回歸的診斷方法做了一定的介紹。論文先簡要介紹了前一類方法，，并對該類方法進行了總結(jié)，指出各種方法在應(yīng)對不同異常值診斷時存在的缺陷，進而引出后一類方法，本文的重點也在于研究回歸分析中穩(wěn)健的異常值診斷方法，通過模擬，研究各種方法在異常值診斷中的效率，并且將幾種常用穩(wěn)健診斷方法的效率進行比較，探討不同異常值出現(xiàn)的情況下，最為有效的診斷方法。 論文共分六部分，首先是緒論部分，主要給出回歸分析中有關(guān)異常值的綜述總結(jié)；第二部分主要介紹有關(guān)異常值的定義、分類及各種異常值對回歸分析結(jié)果的影響；第三部分主要討論目前對回歸分析中異常值診斷和處理的方法以及各種方法的適用性和不足；第四部分通過模擬出各種情況的異常值，在簡單回歸模型和多元回歸模型中分別采用常用的幾種異常值診斷方法，將各個方法的診斷效率進行比較；第五部分給出真實案例并進行分析；最后介紹本文的結(jié)論、不足及未來的工作。
[Abstract]:Regression analysis is a statistical method of analyzing data to understand whether two or more variables are correlated, the direction and intensity of the correlation, and to establish mathematical models to observe specific variables to predict. Controls variables of interest to researchers. Since the establishment of classical linear regression model theory, it has been widely used in many fields, such as natural science and social science, and many achievements have been made. However, when applying regression analysis, there are often outliers, which will directly affect whether the regression model we make can fit well with the reality and the accuracy of parameter estimation. The stability of the model is a series of problems related to regression analysis itself. Therefore, the diagnosis and treatment of outliers is a problem of both theoretical and practical significance. The diagnostic methods of outliers have been paid much attention by scholars, but so far, there is not a standard or widely applicable method. In this paper, two widely used methods for diagnosing outliers are introduced, which are based on LS and robust regression. In this paper, the former method is briefly introduced, and the method is summarized. The defects of each method in dealing with different outliers diagnosis are pointed out, and then the latter kind of method is introduced. The emphasis of this paper is also to study the robust outliers diagnosis method in regression analysis. Through simulation, the efficiency of various methods in outlier value diagnosis is studied, and the efficiency of several commonly used robust diagnostic methods is compared. The most effective diagnostic method is discussed in the case of different outliers. The thesis is divided into six parts, the first part is the introduction part, mainly gives the summary of the abnormal value in the regression analysis, the second part mainly introduces the definition of the abnormal value, the classification and the influence of all kinds of abnormal value on the result of regression analysis. The third part mainly discusses the current methods of diagnosing and dealing with outliers in regression analysis, and the applicability and deficiency of various methods. In the fourth part, the outliers of various situations are simulated. In the simple regression model and the multivariate regression model, we use several commonly used outlier diagnosis methods to compare the diagnostic efficiency of each method; the fifth part gives the real case and analysis; finally, the conclusion of this paper is introduced. Insufficient and future work.
【學(xué)位授予單位】：蘭州商學(xué)院
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224

【參考文獻】

相關(guān)期刊論文 前6條

1 呂恕;朱宏;;統(tǒng)計數(shù)據(jù)中異常值的檢驗方法討論[J];東北師大學(xué)報(自然科學(xué)版);1993年03期

2 趙慧,甘仲惟,肖明;多變量統(tǒng)計數(shù)據(jù)中異常值檢驗方法的探討[J];華中師范大學(xué)學(xué)報(自然科學(xué)版);2003年02期

3 郭亞帆;杜金柱;;經(jīng)典回歸與穩(wěn)健回歸方法的應(yīng)用比較研究[J];內(nèi)蒙古財經(jīng)學(xué)院學(xué)報;2010年04期

4 王懷亮;;回歸診斷在統(tǒng)計數(shù)據(jù)異常值探測中的應(yīng)用[J];黑龍江對外經(jīng)貿(mào);2011年02期

5 樓潤瑜;吳江云;王水生;鐘繼;;檢測數(shù)據(jù)異常值判斷方法的優(yōu)選[J];檢驗檢疫科學(xué);2008年06期

6 Serif HEKIMOGLU;R. Cuneyt ERENOGLU;Jan KALINA;;Outlier detection by means of robust regression estimators for use in engineering science[J];Journal of Zhejiang University(Science A:An International Applied Physics & Engineering Journal);2009年06期

相關(guān)碩士學(xué)位論文 前2條

1 孫廣山;線性回歸模型影響分析及異常點的統(tǒng)計診斷[D];東北林業(yè)大學(xué);2011年

2 王玉梅;線性回歸模型中的異常點分析[D];華中科技大學(xué);2006年

本文編號：1818358