Review of Probability. Sampling distributions, distribution of function of random variables. Weak and Strong laws of large numbers. Estimation of Parameters. Point Estimation. Minimum mean square error (MSE), minimum variance unbiased estimator (MVUE) - Sufficient statistics, Factorisation lemma, minimal sufficient statistics. Obtaining MVUE for one parameter exponential family, Rao Cramer lower bound, Lehmann Scheffe theorem, Complete statistic, Rao Blackwell lehmann Scheffe theorem (RBLS). Maximum likelihood estimation (MLE) and its properties, consistency .. Interval estimation, confidence level. Testing of hypotheses. The type 1 type 2 error, Neymann pearson lemma for obtaining the most powerful (MP) test. Construction of different MP tests. Maximum likelihood testing. ANOVA test and regression test using maximum likelihood testing procedure.
krishna.maddaly@ashoka.edu.in