Aspects of Composite Likelihood Estimation And Prediction

A composite likelihood is usually constructed by multiplying a collection of lower dimensional marginal or conditional densities. In recent years, composite likelihood methods have received increasing interest for modeling complex data arising from various application areas, where the full likelihood function is analytically unknown or computationally prohibitive due to the structure of dependence, the dimension of data or the presence of nuisance parameters. In this thesis we investigate some theoretical properties of the maximum composite likelihood estimator (MCLE). In particular, we obtain the limit of the MCLE in a general setting, and set out a framework for understanding the notion of robustness in the context of composite likelihood inference. We also study the improvement of the efficiency of a composite likelihood by incorporating additional component likelihoods, or by using component likelihoods with higher dimension. We show through some illustrative examples that such strategies do not always work and may impair the efficiency. We also show that the MCLE of the parameter of interest can be less efficient when the nuisance parameters are known than when they are unknown. In addition to the theoretical study on composite likelihood estimation, we also explore the possibility of using composite likelihood to make predictive inference in computer experiments. The Gaussian process model is widely used to build statistical emulators for computer experiments. However, when the number of trials is large, both estimation and prediction based on a Gaussian process can be computationally intractable due to the dimension of the covariance matrix. To address this problem, we propose prediction methods based on different composite likelihood functions, which do not require the evaluation of the large covariance matrix and hence alleviate the computational burden. Simulation studies show that the blockwise composite likelihood-based predictors perform well and are competitive with the optimal predictor based on the full likelihood.Ph