Author Description

This dissertation, "Likelihood-based Methods for Constrained Parameter Problems" by Da, Ju,, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Truncated observations for some applications and parameters with a certain kind of constraints may provide a kind of prior information for the data analysis. Such information, if integrated into the scientific study, can significantly improve the result of statistical inferences. In order to sufficiently utilize such information, these truncations or constraints are taken into consideration in the modeling process. This thesis, therefore, aims to analyze truncated normal data and to study the constrained parameter problems. In practice, the normal distribution is widely used to model continuous data. However, when the data fall in a certain interval, truncated normal distribution becomes a better choice. Through stochastically representing the normal random variable as a mixture of a truncated normal random variable and its complementary random variable, Chapter 2 proposes two new expectation-maximization (EM) algorithms to calculate maximum likelihood estimates of parameters in truncated normal distribution. Furthermore, in the analyses of two real datasets based on Akaike information criterion (AIC) and Bayesian information criterion (BIC), it is found that the truncated normal distribution performs better than the half normal, the folded normal and the folded normal slash distributions. Although Type I multivariate zero-inflated Poisson (ZIP) distribution has been recently proposed to model zero inflated correlated multivariate discrete data by Liu and Tia