Course info

Module 1
1.1 Basic concepts in statistical hypotheses testing-simple and composite hypothesis, critical regions, Type-I and Type-II errors, Significance level, p-value, and power of a test. 1.2 Neyman-Pearson lemma and its applications; 1.3 Construction of tests using NP lemma- Most powerful test, uniformly most powerful test.1.4 Monotone Likelihood ratio and testing with MLR property; Testing in one-parameter exponential families-one sided hypothesis, 1.5 Unbiased and Uniformly Most Powerful Unbiased tests for different two-sided hypothesis; Extension of these results to Pitman family when only upper or lower end depends on the parameters.
Module 2
2.1 Similar regions tests, Neymann structure tests, Likelihood ratio (LR) criterion and its properties, 2.2 LR tests for testing equality of means and variances of several normal populations. Testing in multi-parameter exponential families-tests with Neyman structure, 2.3 UMP and UMPU similar size-tests; 2.4  Confidence sets, UMA and UMAU confidence sets, Construction of UMA and UMAU confidence sets using UMP and UMPU tests respectively.
Module 3
3.1 Sequential probability ratio tests (SPRT), Properties of SPRT, Determination of the boundary constants 2.2 Construction of sequential probability ratio tests, Wald’s fundamental identity, 3.3 Operating characteristic (OC) function and Average sample number (ASN) functions for Normal Binomial, Bernoulli’s, Poisson and exponential distribution.
Module 4
4.1 Notion of likelihood ratio tests, Hotellings-T 2 and Mahalnobis-D 2 statistics-Their properties, interrelationships and uses, 4.2 Null distributions (one sample and two sample cases), Testing equality of mean vectors of two independent multivariate normal populations with same dispersion matrix,4.3 Problem of symmetry, Multivariate Fisher- Behren problem.