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研究生: 黃品勝
論文名稱: 具遺漏值之連續與順序變數混合資料的馬氏距離估計
Estimating of Mahalanobis distances for mixed continuous and ordinal data with missing values
指導教授: 鄭宗記
學位類別: 碩士
Master
系所名稱: 商學院 - 統計學系
Department of Statistics
論文出版年: 2016
畢業學年度: 104
語文別: 中文
論文頁數: 38
中文關鍵詞: 馬氏距離遺漏值混合資料多重插補
外文關鍵詞: Mahalanobis distances, missing value, mixed data, multiple imputation
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  • Bedrick, Lapodus和Powell(2000)提出利用常態潛在變數模型(normal latent variable model),估計連續與順序變數混合型資料(mixed data)馬氏距離(Mahalanobis Distance)的方法,在本論文中沿用相同方法來估計具遺漏值混合型資料馬氏距離,利用一般位置模型(general location model)進行多重插補(multiple imputation)的方法,藉由模擬資料與實例分析,來評估此方法用於處理估計具遺漏值混合型資料馬氏距離。


    Bedrick, Lapodus, and Powell(2000) apply the normal latent variable model to estimate the Mahalanobis distances for mixed continuous and ordinal data. In this thesis, we extend the similar idea by applying general location model and multiple imputation to estimate the Mahalanobis distances for mixed countinuous and ordinal data with missing value. Simulation and real data are used to evaluate the proposed method.

    第一章 緒論1
    1.1研究背景與動機………………………………………………………1
    1.2研究目的………………………………………………………………2
    1.3論文架構………………………………………………………………3
    第二章 一般位置模型與多重插補4
    2.1一般位置模型(general location model)與最大概似估量……………4
    2.2 EM演算法……………………………………………………………5
    2.2.1預測機率函數…………………………………………………6
    2.2.2一般位置模型下EM演算法…………………………………8
    2.3多重插補(multiple imputation)…………………………………………9
    2.3.1多重插補統計推論……………………………………………9
    第三章 估計混合型資料馬氏距離11
    3.1混合型資料馬氏距(Mahalanobis distances)………………………11
    3.2估計混合型資料馬氏距離……………………………………………13
    3.3馬氏距離估計量統計推論……………………………………………15
    第四章 估計具遺漏值混合型資料馬氏距離與模擬分析17
    4.1具遺漏值時一般位置模型下多重插補的馬氏距離估計……………17
    4.2模擬分析………………………………………………………………22
    第五章 實例分析………………………………………………………………….29
    第六章 結論與後續研究………………………………………………………….36
    參考文獻…………………………………………………………………………37

    Bar-Hen, A. and Daudin, J. J. (1995). Generalization of the Mahalanobis Distance in
    The Mixed Case. Journal of Multivariate Analysis, 53, 332-342

    Bedrick, E. J., Lapidus, J. and Powell, J. F. (2000). Estimating the Mahalanobis Dista-
    Nce from Mixed Continuous and Discrete Data. Biometric 56, 394-401.

    Byar, D. P., Green S. B. (1980). The choice of treatment for patients based on covari-
    ate information: application to prostate cancer. Bull du Cancer 67,477-490

    Dempster, A. P., Laird, M., Rubin, D. B. (1977). Maximum likelihood from incompl-
    Ete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-38

    De Maesschalck, R., Jouan-Rimbaud, D. and Massart, D. L. (2000). The Mahalanobis
    Distance, Chemometrics and Intelligent Laboratory Systems 50, 1-18

    Hunt L. and Jorgensen M. (1999). Mixture model clustering using the multimix progr-
    am. Australia and New Zealand Journal of Statistics 41,153-171

    Schafer J. L. (1977). Analysis of Incomplete Multivariate Data, CHAPMAN and HA-
    LL

    Kullback, S. (1959). Information Theory and Statistical. New-York: Dover.

    Krzanowski, W. J. (1983). Distance between population using mixed continuous and
    categorical variable. Biometrika 70, 235-243

    Kenne Pagiui, E. C. and Canale, A. (2014). Pairwise likelihood inference for multiva-
    Riate categorical responses. Technical Report, Department of Statistics, Univers-
    ity of Padua

    Little, R. J. A. and Rubin, D. B. (1989). The analysis of social science data with miss-
    ing values. Sociological Methods and Research, 18, pp. 292-326

    Many, B. F. J. (1994). Multivariate Statistical Method: A Prime, 2nd edition. New Yo-
    rk : Chapman amd Hall.

    Mahalanobis, P. C.(1936). On the generalized distance in statistics, Proceedings of
    the National Institute of Science India, 2, 49–55.

    McParland,D.and Gormley,I.C. (2014). Model base clustering for mixed data:cluster-
    MD.Technical,University College Dublin.

    Olkin, I. and Tate, R. F. (1961). Multivariate correlation models with mixed discrete
    and continuous variables. Annals of Mathematical Statistics 32,448-465

    Poon, W. Y. and Lee, S. Y. (1987). Maximum likelihood estimation of multivariate
    polychoric correlation coefficients. Psychometrika 52, 409-430.

    Rao, C. R (1973). Linear Statistic Inference and Its Applications, 2nd edition. New
    York :Wiley.

    Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592

    Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. Wiley, New
    York

    Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New
    York: Wiley.

    Scafer,J.L(1999). Multiple imputation: a primer. Statiscal methods in medical resear-
    ch, 8(1), 3-15

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