Parameter estimation for ranking data with Markov chain Monte Carlo stochastic approximation

Estimation of parametric models is an important aspect of statistics. In recent decades, with development of high-speed computing technology, the methodology of statistical computing has greatly advanced. This thesis uses the Markov chain Monte Carlo methods and stochastic approximation algorithms (MCMC-SA) to investigate parameter estimation problems in two classes of statistical models. The Thurstonian models are popular and particularly well suited for analyses of ranking data. However, their maximum likelihood estimation has not fully developed before due to the difficulty of computing high-dimensional integration. We show how to use the MCMC-SA algorithm to compute the maximum likelihood estimates for this class of models. Moreover, we demonstrate our methods using the Hong Kong horse racing data. Another important class of models is the frailty models which are very popular in biostatistics. We propose a unified approach to estimate the regression parameters and frailty parameters in various frailty distributions such as Gamma, inverse-Gauss and log-normal. Simulation and real examples all prove that our approach works well.