MAT 684 - Statistics I

Syllabus for MAT 684 – Statistics I

Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 201 (Probability & Statistics) or equivalent

Overview: This course builds on a standard undergraduate probability and statistics course in two ways. First, it makes probability more rigourous by using the concept of measure. Second, it discusses more advanced topics such as multivariate regression, ANOVA and Markov Chains.

Detailed Syllabus:

1. Probability: Axiomatic approach, conditional probability and independent events
2. Random Variables – Discrete and continuous. Expectation, moments, moment generating function
3. Joint distributions, transformations, multivariate normal distribution
4. Convergence theorems: convergence in probability, Weak law of numbers, Borel- Cantelli lemmas, Strong law of large numbers, Central Limit Theorem
5. Random Sampling & Estimators: Point Estimation, maximum likelihood, sampling distributions
6. Hypothesis Testing
7. Linear Regression, Multivariate Regression
8. ANOVA
9. Introduction to Markov Chains

References:

• Statistical Inference by Casella and Berger. Brooks/Cole, 2007. (India Edition)
• An Intermediate Course in Probability by Allan Gut. Springer, 1995.
• Probability: A Graduate Course by Allan Gut. Springer India.
• Measure, Integral and Probability by Capinski and Kopp. 2^nd edition, Springer, 2007.