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題名 參數化Markov鏈上的自助法
Bootstrapping Markov chains for parametric case作者 何秀敏 貢獻者 傅承德
何秀敏日期 1991
1990上傳時間 2-May-2016 17:07:38 (UTC+8) 摘要 設{ Xn ; n ? o } 為一不可約，單一週期及正常返(irreducible, aperiodicand positive recurrent) 的Markov 鏈，令其狀態空間(state space) S 為有限及移轉矩陣(transitionprobability matrix) P. 假設Pij’S 是某一個未知參數θ的函數，且此函數為已知，稱之為PjJ (θ) ，其值域屬於RK ，並令π是它的平接機率(stationary probability) ，給定一組己知的觀察值{ Xn; 0 ?j? n }，令θn 為θ 的最大概似估計(maxirnumlikelihood estimator). 在本論文中，我們要利用自助法 參考文獻 References 1. Anderson, T. and Goodman, L. (1957). Statistical inference about Markov chains. Ann. Math. Statist. 28, pp. 89-110. 2. Athreya, K. B. and Fuh, C. D. (1989). Bootstrapping Markov chains: Countable case. Technical Report: B-89-7, Institute of Statistical Science, Academia Sincia, Taipei, Taiwan, ROC. 3. Bartlett, M. S. (1951). The frequency goodness of fit test for probability chains. Proc.Carnb. Phil. Soc. 47, pp. 86-95. 4. Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical inference for stochastic processes. Academic Press, New York. 5. Billingsley, P. (1961). Statistical inference for Markov Processes. The University of Chicago Press, Chicago. 6. Cinlar, E. (1975). Introduction to Stochastic Processes. pp. 106-168. Prentice-Hall, Englewwood Cliffs, N. J. 7. Doob, J. L. (1953). Stochastic processes. p.228 and p.232. Springer- Verlag, Berlin. 8. Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia. 9. Kulperger, R. J. and Prakasa Rao, B. L. S. (1990). Bootstrapping a finite state Markov chains. Sankhya A 51, Pt. 2, pp. 178-191. 10. Kemeny, J. G. and Snell, J. L. (1960). Finite Markov chains. pp. 69-71. SpringerVerlage,New York. 11. Rao, C. R. (1973). Linear statistkal inference and its applications. pp. 363-366. Wieley: New York. 描述 碩士
國立政治大學
應用數學系資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002005104 資料類型 thesis dc.contributor.advisor 傅承德 zh_TW dc.contributor.author (Authors) 何秀敏 zh_TW dc.creator (作者) 何秀敏 zh_TW dc.date (日期) 1991 en_US dc.date (日期) 1990 en_US dc.date.accessioned 2-May-2016 17:07:38 (UTC+8) - dc.date.available 2-May-2016 17:07:38 (UTC+8) - dc.date.issued (上傳時間) 2-May-2016 17:07:38 (UTC+8) - dc.identifier (Other Identifiers) B2002005104 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/89768 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description.abstract (摘要) 設{ Xn ; n ? o } 為一不可約，單一週期及正常返(irreducible, aperiodicand positive recurrent) 的Markov 鏈，令其狀態空間(state space) S 為有限及移轉矩陣(transitionprobability matrix) P. 假設Pij’S 是某一個未知參數θ的函數，且此函數為已知，稱之為PjJ (θ) ，其值域屬於RK ，並令π是它的平接機率(stationary probability) ，給定一組己知的觀察值{ Xn; 0 ?j? n }，令θn 為θ 的最大概似估計(maxirnumlikelihood estimator). 在本論文中，我們要利用自助法 zh_TW dc.description.tableofcontents 1. Introduction....................1 2. The Bootstrap Method....................2 3. Markov Model....................5 4. Bootstrapping the Parametric Transition Probability of a Markov Chain....................9 5. The Proof of Theorem1....................11 6. Some Numerical Simulations....................16 References....................20 Appendix....................21 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002005104 en_US dc.title (題名) 參數化Markov鏈上的自助法 zh_TW dc.title (題名) Bootstrapping Markov chains for parametric case en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) References 1. Anderson, T. and Goodman, L. (1957). Statistical inference about Markov chains. Ann. Math. Statist. 28, pp. 89-110. 2. Athreya, K. B. and Fuh, C. D. (1989). Bootstrapping Markov chains: Countable case. Technical Report: B-89-7, Institute of Statistical Science, Academia Sincia, Taipei, Taiwan, ROC. 3. Bartlett, M. S. (1951). The frequency goodness of fit test for probability chains. Proc.Carnb. Phil. Soc. 47, pp. 86-95. 4. Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical inference for stochastic processes. Academic Press, New York. 5. Billingsley, P. (1961). Statistical inference for Markov Processes. The University of Chicago Press, Chicago. 6. Cinlar, E. (1975). Introduction to Stochastic Processes. pp. 106-168. Prentice-Hall, Englewwood Cliffs, N. J. 7. Doob, J. L. (1953). Stochastic processes. p.228 and p.232. Springer- Verlag, Berlin. 8. Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia. 9. Kulperger, R. J. and Prakasa Rao, B. L. S. (1990). Bootstrapping a finite state Markov chains. Sankhya A 51, Pt. 2, pp. 178-191. 10. Kemeny, J. G. and Snell, J. L. (1960). Finite Markov chains. pp. 69-71. SpringerVerlage,New York. 11. Rao, C. R. (1973). Linear statistkal inference and its applications. pp. 363-366. Wieley: New York. zh_TW
