Theory of Inference-I

Syllabus Details

• Problem of Point Estimation: Properties of point estimation: unbiasedness, closeness, mean squared error, consistency and BAN; methods of finding estimators: method of moments, maximum likelihood, other methods; sufficient, complete and ancillary statistics; unbiased estimation: lower bound for the variance of an estimator; location and scale invariant estimators; optimum properties of maximum likelihood estimation.
• Parametric Interval Estimation: Definition of confidence interval, pivotal quantity; sampling from the normal distribution: confidence interval for the mean, confidence interval for the variance, simultaneous confidence region for the mean and variance, confidence interval for difference in means; methods of finding confidence intervals: pivotal quantity method, statistical method, large sample confidence intervals.

Course Learning Objective

1. Discuss the concept of point estimation and its properties.
2. Apply sufficiency, ancillarity and likelihood principles.
3. Understand Fisher information, lower bounds to the variance of estimators, and MVUE.
4. Discuss the concept of interval estimation and its properties.
5. Determine the shortest expected length confidence interval.

Recommended Books

1. Rohatgi, V. K. An Introduction to Probability and Statistics. Wiley Eastern, 1985
2. Casella, G. and Berger, R. L. Statistical Inference. 2nd ed. Academic Internet Pub., 2002
3. Mood, A. M., Graybill, F. A. and Boes, D. C. Introduction to the Theory of Statistics. 3rd ed. McGraw-Hill, 1974
4. Lehmann, E. L. Theory of Point Estimation. John Wiley, NY, 1983
5. Lehmann, E. L. Testing Statistical Hypotheses. John Wiley & Sons, 1986
6. Ferguson, T. S. Mathematical Statistics. Academic Press, 1967
7. Kale, B. K. A First Course on Parametric Inference. Narosa Publishing House, 1999