| The thesis consists of three topics on the nonstandard likelihood inference: theory on impact of nuisance parameters, likelihood inference based on the misspecified model and efficient composite likelihood estimation.;The first part deals with the impact of nuisance parameters. In a parametric model, parameters are typically partitioned as parameters of interest and nuisance parameters respectively. In the likelihood based inference framework, several authors propose adjusted profile likelihoods to reduce the sensitivity to nuisance parameters. However, as the data structure becomes more complex, the inference based on the full likelihood may be inconvenient. Due to computational intractability and model misspecification, many nonstandard likelihood methods which include pseudo likelihood, composite likelihood and likelihood from a misspecified model, have been developed. Nevertheless, the modification of the nonstandard likelihood in the presence of nuisance parameters is rarely mentioned in the literature. The purpose of the first part is to suggest a simple adjustment to the nonstandard likelihood under this circumstance. The impact of nuisance parameters is considerably reduced when adopting the proposed approach. The adjustment is still novel even if attention is restricted to the profile likelihood. Finally, the advantages of the modification are illustrated through examples and reinforced through simulations.;The second part focuses on the likelihood based inference under model misspecification. In reality, the model which characterizes the true underlying phenomenon may be complicated. Due to heavy computational burden and potential misspecification of the true model, a simpler but misspecified model is often used in practice. In the second part, we propose a unified approach to correct the bias of the estimator and perform likelihood inference based on the misspecified model. In particular, to deal with nuisance parameters, we introduce a pseudo likelihood approach as well as a sensitivity analysis approach. We also evaluate the possible misspecification of the nuisance parameters. The corresponding asymptotic properties are examined and the finite sample performances are considered through several examples, simulations and real data analysis.;The third part involves the composite likelihood. How to construct a composite likelihood retaining high efficiency is a major issue in the composite likelihood literature. In the third part, we consider an empirical likelihood approach to combine the information from the marginal and pairwise score functions in the context of correlated data. Several types of empirical likelihoods are proposed to make inference on the marginal and association parameters. The resulting empirical likelihood methods are more efficient than the independent and pairwise likelihood methods. The efficiency improvement is confirmed by the simulation studies and the analysis of a real data set. |
