## Details of MA4107 (Autumn 2019)

 Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA4107 Statistical Inference Anirvan Chakraborty

Syllabus
Common Families of Distributions: Location and scale families, exponential families.

Principles of Data Reduction: Introduction, sufficient statistics, minimal sufficient statistics, ancillary statistics, complete statistics, relation between ancillary and complete sufficient statistics.

Point Estimation: Introduction, maximum likelihood estimators, EM algorithm; Methods of evaluating estimators-- mean squared error, uniformly minimum variance unbiased estimator (UMVUE), sufficiency and unbiasedness, loss function optimality, asymptotic evaluations, consistency, efficiency.

Hypothesis Testing: Introduction; Methods of finding tests-- likelihood ratio tests, Bayesian tests, union-intersection and intersection-union tests, Methods of evaluating tests-- error probabilities and the power function, most powerful tests, sizes of union-intersection and intersection-union tests, p-values, loss function optimality.

Interval Estimation: Introduction; Methods of finding interval estimators-- pivotal quantities, pivoting the CDF; Methods of evaluating interval estimators-- size and coverage probability, test-related optimality, loss function optimality.

Prerequisite
Analysis IV (MA3204) and Statistics I (MA3205)

References
Suggested Texts:

1. Casella, G. and Berger, R.L., Statistical Inference, Thomson Brooks/Cole.

2. Cramer, H., Mathematical Methods of Statistics, Princeton University Press.

3. Lehman, E.L. and Casella, G., Theory of Point Estimation, Springer.

4. Lehman, E.L. and Romano, J.P., Testing Statistical Hypotheses, Springer.

5. Rao, C.R., Linear Statistical Inference and Its Applications, Wiley-Interscience.

6. Rohatgi, V.K., Statistical Inference, Dover Publications.

7. Wilks, S.S., Mathematical Statistics, Buck Press.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 7 Elective
7 RS 1 Not Allowed
8 RS 2 Not Allowed