Keywords: General transformation model, Model Misspecification, Marginal likelihood, Markov chain Monte Carlo, Stochastic approximation, Mixed-effects model, Consistency, Asymptotic normality, Discretization technique. / Part II of this thesis concerns studies of mixed-effects general transformation models, i.e. general transformation models incorporating both fixed and random effects, to analyze grouped or clustered data. Rank-based marginal likelihood estimation is proposed. The estimation procedure is baseline-free, a good property enjoyed by the Cox partial likelihood. A three-stage Markov chain Monte Carlo stochastic approximation (MCMC-SA) algorithm is developed to find the maximum marginal likelihood estimation (MMLE). The asymptotic normality is obtained via a discretization procedure. Monte Carlo simulation shows that the MMLE has a good small- and moderate-sample behavior. In the end we illustrate an application of the proposed method to Hong Kong horse racing data. / Since it was first proposed by Dabrowska and Doksum in 1988, there is an explosive growth in both studies and applications of transformation model. Transformation model has many naturally endowed merits such as flexibility and conciseness in modeling lifetime or duration and ranking data involving covariates. However, like many other statistical models, transformation model may suffer the problem of misspecification due to falsely specified error term distribution or omitted covariates. The author investigates the large sample behavior of the rank-based quasi maximum marginal likelihood estimator (QMMLE) when transformation model is misspecified, and shows that owing to model misspecification, the QMMLE converges not to the true value of the parameter of interest, but to a "pseudo-true value" which minimizes the Kullback-Leibler divergence between the true model and the misspecified working model. A robust "sandwich" estimate of variance is proposed. The asymptotic normality of the QMMLE is also proved. Following the steps of White (1982), the appropriate Wald test statistic, Lagrange Multiplier test statistic and Information matrix specification test statistic are proposed. / Ni, Zhongxin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3587. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 86-99). / 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_344255 |
| Date | January 2008 |
| Contributors | Ni, Zhongxin., 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 (viii, 99 leaves : 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/) |
Page generated in 0.0019 seconds