- Semester: III
- Number of Credits: 4
Preamble
This course aims to familiarize students with elements of probability and inferential statistics that form the basis of modern econometrics. This course is a bridge between what is taught in the core paper and more advanced treatments of the subject.
The four credit paper will be offered in the third semester.
1. Axiomatic Approaches to Probability (08 lectures): Sample spaces, sigma fields and probability measure- Probability Axioms and their Implications- Counting methods- Conditional probability, independence and exchangeability- Bayes’ Theorem and its Applications
2. Random Variables and Probability Distributions (16 lectures): The concept of a random variable- joint, marginal and conditional distributions-Moment generating function and cumulants- Independent random variables- Some discrete and continuous random variables (normal, t, chi square and F distributions mandatory)- Functions of random variables.
3. Introduction to Statistical Inference (16 lectures): Modes of Convergence- Weak and strong law of large numbers – Central limit theorem with proof- Properties of estimators- Different Estimation methods and the properties of the associated estimators ( Multiple OLS estimators mandatory)-Introduction to Bayesian inference
4. Hypothesis testing Theory (08 lectures): UMP tests and unbiased tests- simple null versus composite hypotheses- Likelihood ratio test- Wald Test- Lagrange Multiplier Tests- Tests of restrictions in an OLS framework and their applications.
References
1. |
Rohatgi Vijay (2003): Statistical Inference, Dover, New York. |
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2. |
Nachane D.M. (2006): Econometrics: Theoretical Foundations and Empirical Perspectives, Oxford, Delhi. |
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