**DESCRIPTION OF COURSES**

**AS 563 STATISTICAL INFERENCE (4L+1P) III
(Pre-requisite : AS 562)**

**Objective**

This course lays the foundation of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They would also be given the concepts of nonparametric and sequential test procedures and elements of decision theory.

**Theory**

UNIT I

Point estimation, Properties of estimators: unbiasedness, consistency, efficiency and sufficiency. Frechet-Cramer-Rao inequality, Rao-Blackwell theorem, completeness and bounded completeness, Basu’s theorem.

UNIT II

Methods of estimation: maximum likelihood, least squares, minimum χ2, minimum distance, moments, maximum entropy.

UNIT III

Testing of hypothesis: randomized and non randomized tests, Neyman-Pearson lemma, power function, uniformly most powerful tests and their constructions, unbiased tests, likelihood ratio tests. Confidence-interval estimation.

UNIT IV

Sequential analysis, sequential probability ratio test. Elements of decision theory and bayesian inference.

UNIT - V

Nonparametric tests: r un, sign, rank, median, Wilcoxon-Mann-Whitney, Kruskal-Wallis, Friedmann two - way ANOVA by ranks.

**Practicals**

Exercises on estimation of parameters using methods of maximum likelihood, minimum χ2 and moments. Obtaining confidence interval estimates, MP and UMP tests, Large sample tests, Non-parametric tests, Sequential probability ratio test, Decision functions.

**Suggested Readings**

- Box, G.E.P. and Tiao, G.C. 1973.
*Bayesian Inference in Statistical Analysis*. Addison Wesely. - Casela, G. and Berger, R.L. 2001.
*Statistical Inference*. Duxbury Thompson Learning. - Christensen, R. 1990.
*Log Linear Models*. Springer. - Conover, W.J. 1980.
*Practical Non-parametric Statistics*. John Wiley. - Dudewicz, E.J. and Mishra, S.N. 1988.
*Modern Mathematical Statistics*. John Wiley. - Gibbons, J.D. 1985.
*Non Parametric Statistical Inference*. Marcel Dekker. - Hogg, R.V. and Craig, T.T. 1978.
*Introduction to Mathematical Statistics*. Macmillan. - Kendall, N.G. and Stuart, A. 1960.
*Advanced Theory of Statistics.*Vol. I. Charles Griffen and Co. Ltd. - Kiefer, J.C. 1987.
*Introduction to Statistical Inference*. Springer Verlag. - Lehmann E.L. 1983.
*Theory of Statistical Hypotheses*. John Wiley. - Lehmann, E.L. 1986.
*Theory of Point Estimation*. John Wiley. - Mood, A.M., Graybill, F.A. and Boes, D.C. 1974.
*Introduction to the Theory of Statistics*. McGraw Hill. - Randles, R.H. and Wolfe, D.A. 1979.
*Introduction to the Theory of Nonparametric Statistics*. John Wiley. - Rao, C.R. 1965.
*Linear Statistical Inference and its Applications*. John Wiley. - Rohatgi, V.K. and Saleh, A.K. 2005.
*An Introduction to Probability and Statistics*. John Wiley. - Rohatgi, V.K. and Saleh, A.K. Md. E. 2005.
*An Introduction to Probability and Statistics*. John Wiley. - Rohtagi, V.K. 1984.
*Statistical Inference*. John Wiley. - Siegel, S., Casellan, Jr. and Johan, N. 1988.
*Nonparametric Statistical Methods for Behavioral Sciences*. McGraw Hill. - Siegel, S., Johan, N. and Casellan, Jr. 1956.
*Non-parametric Tests for Behavior Sciences*. John Wiley & Sons. - Wald, A. 2004.
*Sequential Analysis*. Dover Publications.