Likelihood based estimation

In this thesis we will describe the maximum likelihood method, method of estima- ting unknown parameters that determine the probability distribution of the observed data. We will also introduce other methods derived from the likelihood. We focus pri- marily on a quasi-likelihood and a pseudo-likelihood approach. Then we briefly describe profile likelihood, empirical likelihood, and conditional likelihood. The thesis includes a simulation study which compares the quality of the estimators based on the maximum likelihood and the quasi-likelihood or the maximum likelihood and the pseudo-likelihood using the mean squared error.