Model Selection For Constrained Models And Its Application

This paper consists of five chapters.The introduction is located in Chapter 1.In Chapter 2, we extend the principles of covariance penalties to the field of order restricted statistical inference. For normal means constrained by linear in-equalities, we obtain two new information criteria, ORICP and ORICP*. Simulation studies indicate that ORICP and ORICP* are often more effective than AIC and BIC.In Chapter 3, we develop an information criterion for selecting inequality con-straints on parameters in order-restricted inference. Our new criterion applies to general order restrictions, whereas the earlier proposed information criterion (An-raku,1999) only works for simple order restrictions. We show that, under mild regularity conditions, the proposed information criterion is consistent in selecting the true inequality constraint. In addition, we extend the criterion to the case where parameters of interest are not explicitly defined but given by estimating equations. In such situations, the information criterion can be constructed using empirical likelihood. Simulation studies indicate that our new criterion is often more effective than Anraku's information criterion even when the true inequality constraints are simple order restrictions.In Chapter 4, we propose a computationally efficient information criterion-based clustering algorithm, called ORICC, which takes account of the ordering in time-course microarray experiments by embedding the order-restricted inference into a model selection framework. In addition, we also developed a bootstrap procedure to assess ORICC's clustering reliability for every gene. Simulation stud-ies show that the ORICC method is robust, gives good clustering accuracy and is computationally efficient. We have developed a software package ORIClust to implement ORICC. In Chapter 5, we extend ORICP* to exponential-family models using Kullback-Leibler loss function and discuss adaptive model selection for constrained models.The research of the author is supported by the NSF of China (No.10871037) and Program for New Century Excellent Talents in University (NCET-09-0284).