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題 名 | Bootstrap Method for Censored Markov Chains=設限馬可夫鏈自助法之研究 |
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作 者 | 傅承德; 洪文良; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷 期 | 22:1 1998.01[民87.01] |
頁 次 | 頁1-7 |
分類號 | 319.1 |
關鍵詞 | 設限馬可夫鏈自助法; Bayesian bootstrap; Bootstrap; Censored Markov chains; Product estimator; Transition probability matrix; |
語 文 | 英文(English) |
中文摘要 | 考慮由一具有轉移機率矩陣P�a之非齊次設限馬可夫鏈所獲得的 r 個觀察值 {(X □, J □ ), 0 ≦ n ≦ N,k=1,...,r}。 對於 Aalen and Johansen (1978) 和 Phelan (1988) 所提 P �a的積估計量□�a, 我們使用自助法與貝氏自助法與貝氏自助法近 似□ (□�a -P �a,)0 ≦ n ≦ N,的抽樣分佈,進而建構近似的信賴區間。本文証明在大 樣本時,自助法與貝氏自助法具有第一階漸近性。有關兩者在小樣本的應用情形,本文亦做 了一個模擬研究。 |
英文摘要 | Many population processes in medical clinical trial, demography, epidemiology and other fields can be repesented by censored Markov chain models. The censoring mechanism is generally useful in applications and maintains the conditional multinomial sampling model for successive transitions. In this article, we focus on setting confidence intervals for the unknown parameters of transition probabilities. That is, consider r observations {(X□,J□), 0≦n≦N, k=1,...,r} from a non-homogeneous censored Markov chain, with transition probability matrix P�a. For the product estimator □�aof P�aproposed by Aalen and Johansen (1978) and Phelan (1988), we investigate the behavior of bootstrap and Bayesian bootstrap to approximate the sampling distribution of □(□�a-P�a) for 0≦n≦N, and then construct and approximate confidence interval. The rationale of Bayesian bootstrap is based on the conjugate beta-neutral process prior. The performance of these approximations will be justified using large sample theory as well as small sample simulation. |
本系統中英文摘要資訊取自各篇刊載內容。