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Introduction to Likelihood-Based Estimation and Inference provides a thorough and self-contained introduction to statistical modelling within the framework of the likelihood function.
Based on worked-through examples, the book presents the main principles for estimation of parameters using the likelihood approach, the principles for applying basic probability theory to characterize the stochastic properties of estimators and test statistics, as well as ideas for basic model control and misspecification testing. Examples include models for Bernoulli trials, models for Poisson count data, and the linear regression model as a special case of the likelihood analysis of a Gaussian model.
The book also introduces numerical optimization of the likelihood function, which provides the tools for building and analyzing more complicated – and empirically relevant – cases.