Course Contents

Concepts & Problems of estimation, Properties of Estimators, Methods of estimation (Method of ML, LS, and Bayes) Asymptotic theory of estimation. Confidence intervals and regions, simultaneous confidence intervals, Confidence regions from pivotal quantities, Bayesian interval estimation, Methods of finding confidence intervals. Basic concepts, Asymptotic tests, Neyman Pearson Lemma, Monotone-Likelihood ratio Approach, Exponential class of densities. Hypothesis testing methods: generalized Likelihood Ratio Tests, Asymptotic properties of Generalized Likelihood ratio test, Lagrange’s Multiplier Tests, Wald Test, Test in GLM, Bayes test.

Course Synopsis

To give in depth knowledge to the students regarding statistical inference, enabling them to conduct research.

Course Learning Outcomes

On successful completion of the course the students will be able to • understand probability-based statistical inference. • apply various techniques to minimize variance and bias and have the knowledge of variance- bias tradeoff. • apply parameter optimization algorithms for model fitting.