For discretization method, which provides an effective way to handle the problem, we focus on constructing a discretized version of continuous failure times. The major observation is that discrete failure times with finite values will attain their exact values although only ranks are given, as long as sample size is large enough. The score function can be asymptotically approximated by a sum of independent random variables. Consistency, asymptotic normality and efficiency of estimator can be obtained by using standard results for estimating equations, given some milder and more feasible conditions than those of martingale method. / In this thesis, some finite sample properties of marginal likelihood will be established. We prove under some regular conditions the score function of the marginal likelihood is a martingale, and prove the marginal likelihood satisfies some properties enjoyed by the standard likelihood method, although only use the relative ranks to make inference of the parameter instead of the full information. / In this thesis, the author studies some asymptotic properties of the marginal maximum likelihood estimate (marginal MLE) for general transformation models. The general transformation model is an important class of models for survival times and is nontrivially more general model than the linear transformation model (Gu, Sun and Zuo, 2005). By using marginal likelihood, we obtain estimator of regression parameter which does not depend on its baseline survival function, a property enjoyed by the Cox regression model. The major obstacle for the general transformation models is the resulting estimation function is complicated and usually has no closed analytic expression. Gu etc. (2005) proposed Markov chain Monte Carlo (MCMC) stochastic approximation algorithm to solve the marginal MLE. / Moreover, a discussion is given for the question of asymptotic properties for the proposed marginal MLE based on two different methods: martingale method and discretization method. For martingale method, emphasis is given to the role of martingale limit theory and results presented are primarily theoretical. / We also demonstrate some important transformation models do satisfy our conditions and thus show their consistency, asymptotic normality and efficiency for the first time. / Huang Bin. / "Dec 2005." / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6484. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 63-69). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343739 |
| Date | January 2005 |
| Contributors | Huang, Bin, Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (x, 69 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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