Fall 2016     BSTA622     Advanced statistical inference

Course instructors:

Yong Chen (Part I) and Jinbo Chen (Part II)


Outline of topics:

Parametric Inference:

        Unbiased estimation and unbiased estimating functions

        Maximum likelihood estimation: Consistency, asymptotic normality, and efficiency

        Hypothesis testing: Wald test, Likelihood ratio test, Score test

        Influence functions

        EM algorithm

        Model checking, Model mis-specification, and model selection

        Examples of Non-regular maximum likelihood estimation

        Marginal likelihood, Conditional likelihood, (modified) profile likelihood, composite likelihood, and pseudolikelihood

        U-statistics theory

        Contiguity theory       

        Bayes and Empirical Bayes estimators, Bayesian tests


Semiparametric Inference:

         Semiparametric maximum likelihood estimation (Case-control study; Cox proportional hazards regression)


         Generalized score test, with Pearson’s Chi^2 test as an example

         Semiparametric inference with incomplete data

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