政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/30926

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/30926

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题名:	混合連續與間斷資料之馬式距離的穩健估計 Robust estimation of the Mahalanobis distance for multivariate data mixed with continuous and discrete variables
作者:	任嘉珩 Jen , Chia Heng
贡献者:	鄭宗記任嘉珩 Jen , Chia Heng
关键词:	混合型資料隱藏常態變數模型穩健估計馬式距離 mixed data normal latnet variable model robust estimation Mahalanobis distacne minimum covariance determinant
日期:	2007
上传时间:	2009-09-14
摘要:	本研究採用Lee 和Poon 所提出的隱藏常態變數模型來估計混合連續與間斷型變數之參數估計，並估計其馬式距離。此外，並利用穩健估計來估計混合型資料參數及其馬式距離，可在有離群值時解決最大蓋似估計的不穩定。 Poon and Lee (1987) applied normal latent variable model to deal with the parameters estimation for the data mixed with continuous and discrete variables and Bedrick et al. (2000) used this idea to evaluate the Mahalanobis distance. In this thesis, we extend a similar idea to robustly estimate Multivariate Data Mixed with Continuous and Discrete Variables with the same model. Furthermore, we evaluate the Mahalanobis distance which can determine similarity of variables. The proposed method can overcome the unreliability of MLE while there exist outliers in the data.
參考文獻:	[1] Barnett, V. and Lewis, T. (1994), Outliers in Statistical Data, 3rd ed. New York: John Wiley and Sons. [2] Bedrick, E. J., Lapidus, J., and Powell, J. F. (2000), Estimating the Mahalanobis Distance from Mixed Continuous and Discrete Data, Biometrics, 56, 394–401. [3] Bhattacharyya, A. (1943), On a measure of divergence between two statistical populations defined by their probability distributions, Bulletin of the Calcutta Mathematical Society, 35, 99–109. [4] Donoho, D. L., and Huber,P. J. (1983), The Notion of Breakdown Point. In A Festschrift for Erich L. Lehmann, Ed. P. J. Bickel, K. A. Docksum and J. L. Hodges, Jr., 157–84, Belmont CA: Wadsworth. [5] Hampel, F., Ronchetti, P., Rousseeuw, P., and Stahel, W. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: John Wiley and Sons. [6] Huber, Peter. J. (1964), Robust estimation of a location parameter, The Annals of Mathematical Statistics, 35, 73–101. [7] Huber, Peter. J. (1981), Robust Statistics, New York: John Wiley and Sons. [8] Jobsin, J. D. (1992), Applied Multivariate Data Analysis: Volume II: Categorical and Multivariate Methods, New York: Springer-Verlag. [9] Krzanowski, W. J. (1975), Discrimination and classfication using both binary and continuous variables, Journal of the American Statistical Association, 70, 782–790. [10] Krzanowski, W. J. (1983), Distance between population using mixed continuous and categorical variables, Biometrika, 70, 235–243. [11] Lehmann, E. L. and Casella, G. (1998), Theory of Point Estimation, New York: Springer. [12] Krzanowski, W. J. and Marriott, F. H. C. (1995), Kendall’s Library of Statistics 2, Maltivariate Analysis Part 2, London: Arnold. [13] Mahalanobis, P. C. (1936), On the generalized distance in statistics, Proceedings of the National Institute of Science India, 2, 49–55. [14] Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979), Multivariate Analysis, London: Academic Press. [15] Maronna, R. A., Martin, R. D. and Yohai, V. J. (2006), Robust Statistics, Theory and Methods, New York: Wiley. [16] Matusita, K. (1972), Discrimination and the affinity of distributions, Sidcriminant Analysis and Applications, Ed. T. Cacoullos, pp.213-223, New York: Academic Press. [17] Olkin,I. and Tate, R. F. (1961), Multivariate correlation models with mixed discrete and continuous variables, Annals of Mathematical Statistics, 32, 448– 465. [18] Poon, W. Y. and Lee, S. Y. (1986), Maximum likelihood estimation of polyserial correlations, Psychometrika, 51, 113–121. [19] Poon, W. Y. and Lee, S. Y. (1987),Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients, Psychometrika, 52, 409– 430. [20] Prohorov, Y. V. (1956), Convergence of random processes and limit theorems in probability theory, Theory of Probability and its Applications, 1, 157–214. [21] Rousseeuw, P. J. (1984), Least median of squares regression, Journal of the American Statistical Association, 79, 871–880. [22] Rousseeuw, P. J. and A. M. Leroy (1987), Robust Regression and Outlier Detection, New York: John Wiley. [23] Rousseeuw, P. J. and Van Driessen, K. (1999), A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212V223. [24] Zaman, A., Rousseeuw, P. J., and Orhan, M. (2001), Econometric applications of high-breakdown robust regression techiniques, Econometrics Letters, 71, 1–8.
描述:	碩士國立政治大學統計研究所 95354024 96
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0095354024
数据类型:	thesis
显示于类别:	[統計學系] 學位論文

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