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研究生:劉華坤
研究生(外文):Hua-Kun Liu
論文名稱:雙變量關聯模型下參數估計之D-與Ds-最適設計
論文名稱(外文):D- and Ds-optimal Designs for Estimation of Parameters in Bivariate Copula Models
指導教授:羅夢娜羅夢娜引用關係
指導教授(外文):Mong-Na Lo Huang
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:58
中文關鍵詞:二維現時狀態數據關聯模型Ds-最適設計檢測時間D-最適設計
外文關鍵詞:Ds-optimal designmonitoring timeBivariate current status dataCopula modelD-optimal design
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對於現時狀態的數據(current status data),真正的失效時間(failure time)可能無法直接被觀察到,這一類型的資料,我們所能得到的資訊是檢測時間(monitoring time)以及失效時間是發生在檢測時間之前或是之後。因此,若想從這一類型的資料中獲得更多的資訊,則檢測時間是非常重要的。在這篇論文中,我們經由實驗設計的方法,根據D-與Ds-之最適設計準則,去尋找最佳的檢測時
間Ci (i =1, … ,n)使得我們在二維的關聯模型之下,可以獲得最多的資訊。然後在Clayton 關聯模型之下,經由模擬分析,所得之模擬數據,再根據這些最佳檢測時間*
D C 和*Ds C ,藉由最大概似函數(maximum likelihood function)估計法,去同時估計這些未知參數的MLE,並比較在D-與Ds-之最適設計下的表現。
For current status data, the failure time of interest may not be observed exactly. The type of this data consists only of a monitoring time and knowledge of whether the failure time occurred before or after the monitoring time. In order to be able to obtain more information from this data, so the monitoring time is very important. In this work, the optimal designs for determining the monitoring times such that maximum information may be obtained in bivariate copula model (Clayton) are investigated. Here, the D-
optimal criterion is used to decide the best monitoring time Ci (i = 1; ¢ ¢ ¢ ; n), then use these monitoring times Ci to estimate the unknown parameters simultaneously by maximizing the corresponding likelihood function. Ds-optimal designs for estimation
of association parameter in the copula model are also discussed. Simulation studies are presented to compare the performance of using monitoring time C¤D and C¤Ds to do the estimation.
Abstract
List of Tables
List of Figures
1 Introduction
2 Preliminaries
2.1 Linear model
2.2 Generalized linear models
2.3 Copula models
2.4 Inferences
3 D- and Ds-optimal designs
3.1 Under independence
3.2 Under association
4 Numerical simulation
4.1 Generating the bivariate current status data
based on a copula model
4.2 Simulation Studies
5 Conclusion
References
Appendix
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University Press, New Y ork.
[2] Chaudhuri, P. and Mykland, P. A. (1993). Optimal design and inference
based on likelihood. Journal of the American Statistical Association, 88,
538-546.
[3] Clayton, D. G. (1978). A model for association in bivariate life tables and
its application in epidemiological studies of familial tendency in chronic disease
incidence. Biometrika, 65, 141-151.
[4] Fedorov, V. V. (1972). Theory of Optimal Experiments. Probability and
mathematical statistics. New Y ork, London, Academic Press.
[5] Genest, C., Ghoudi, K. and Rivest, L. P.(1995). A semiparametric
estimation procedure for dependence parameters in multivariate families
of distributions. Biometrika, 82, 543-552.
[6] Genest, C. and MacKay, R. J.(1986a). Archimedean copulas and bivarate
families with continuous marginals. Canadian Journal of Statistics, 14,
145-159.
[7] Genest, C. and MacKay, R. J.(1986b). The joy of copulas: Bivariate
distributions with uniform marginals. American Statistician, 40, 280-283.
[8] Heise, M. A. and Myers, R. H. (1996). Optimal designs for bivariate
logistic regression. Biometrics, 52, 613-624.
[9] Li, Y. and Wong, K. F. (2006). A semiparametric method for the
analysis of bivariate current status data based on copula model. Technical
report, Institute of Statistics National University of Kaohsiung.
[10] Nelsen, R. B. (1999). An Introduction to Copulas, Springer Series in
Statistics.
[11] Oakes, D. (1989). Bivariate survival models induced by frailties. Journal
of the American Statistical Association. 84, 487-493.
[12] Schweizer, B. and Wol®, E. F. (1981). On nonparametric measure of
dependence for random variables. Annals of Statistics. 9, 879-885.
[13] Shih, J. H. and Louis, T. A. (1995). Inferences on the association
parameter in copula models for bivariate survival data. Biometrics.
51, 1384-1399.
[14] Wang, W. and Ding, A. A. (2000). On assessing the association for
bivariate current status data. Biometrika, 87, 879-893.
[15] Wang, W. (2003). Estimating the association parameter for copula
models under dependence censoring. Journal of the Royal Statistical
Society, Series B. 65, 257-273.
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