Statistical Inference

This course aims at giving the foundation knowledge of Probability and Statistical Inference. In particular, it gives details of theory of Estimation and testing of hypothesis. Both theoretical aspect will be discussed and practical problems will be dealt with in great detail. This course will help students and practitioners of statistics at both UG and PG level. This course will also serve as a foundation course for students workingon Machine Learning. INTENDED AUDIENCE :Students and practitioners of Statistics, MathematicsPREREQUISITES :Background of Probability, Basic Knowledge of Data its collection and descriptive statisticsINDUSTRY SUPPORT :Parameter Estimation and Testing of Hypothesis are basic requirements

Week 1: Revision of Probability, Different Discrete and Continuous Distributions
Week 2: Functions of Random Variables and their distributions, T, Chi-sq, F distributions and their Moments
Week 3: Introduction of statistics and the distinction between Data and its properties, and probabilistic models
Week 4: Estimator and methods of estimation, Properties of an estimator: Consistency, Unbiasedness, Efficiency and Sufficiency
Week 5: Neyman Factorization, Cramer-Rao Bound
Week 6: Confidence Intervals, Concepts of hypothesis testing, Characteristics of Good Hypothesis, null and Alternative Hypotheses, Types of Errors
Week 7: Inference on Population mean, Comparing two population means, Inference on Variance, Comparing two population variance
Week 8: Neyman Pearson Lemma