# SI402: Statistical Inference

**Prof. Rajni Joshi and Prof. Siuli Mukhopadyay**

**Course Description:**

Course will include revision of all concepts thought in SI 417 followed by important concepts used in estimation and hypothesis testing theory. From practical point of view, one should take this course if they want to understand the theoretical formulation of estimation and hypothesis tests and how these principles can be applied to real life data to extract useful information (not much application oriented in this course but one can pick it up on their own from the basics thought). Overall can be a useful course.

**Prerequisites: **

SI 417 – Introduction to probability theory

**Course Content****s:**

1st part (Prof. Rajni)

- Revision of random variables, probability distributions, probability mass and density functions, moment generating function, variable transformations, inequalities, properties of mean and variance, etc.
- Revision of convergence (in probability, distribution, almost surely, etc.)
- Order Statistics and related theory
- Principles of Data Reduction: Sufficient statistics, minimality, sufficiency, ancillary statistics, completeness

2nd part (Prof. Siuli)

- Moment estimation: Asymptotic Theory of Estimation, Maximum likelihood method, method of moments
- Bayes’ estimation theory
- Unbiased estimation, mean square error, Cramer-Rao lower bound
- Likelihood Ratio tests, Uniformly Most powerful tests, Neyman-Pearson lemma
- Hypothesis testing, types of errors, size of test. confidence intervals
- Karlin Rubin Theorem

**Attendance, Course Load and Grading:**

80% attendance required for 1st half of course (under Prof. Rajni), strictly enforced, there were penalties in case attendance was lesser. Attendance not compulsory for 2nd half.

4.5 hours per week of classes and tutorials. Some effort is required per week outside the class also.

Policy: 1st half – 10% quiz, 30% midsem

2nd half – 15% quiz, 45% endsem

**References:**

G. Casella and R.L. Berger, Statistical Inference

**Added Information:**

The 1st half of the course is relatively difficult and effort is required to understand the concepts and score well in the exams. The 2nd half of the course is relatively easier and once can do well if they have done the tutorials and gone through the notes thoroughly.

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