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Theory of Inference-II

Course Code: IM 402; ST 502  |  Credits: 4  |  Prerequisite: Theory of Inference-I

Syllabus Details

  • Unit I:(Asymptotic Theory of Estimation) Consistency and asymptotic relative efficiency of estimators; consistent asymptotic normal (CAN) estimator; method of maximum likelihood; CAN estimator for one parameter Cramer family; Cramer–Huzurbazar theorem; solutions of likelihood equations; method of scoring; Fisher lower bound to asymptotic variance; MLE in Pitman family and double exponential distribution; MLE in censored and truncated distributions.
  • Unit II:(Tests for Composite Hypotheses) Similar tests; Neyman structure; UMPU tests for composite hypotheses; invariance tests and UMP invariant tests; likelihood ratio test; asymptotic distribution of LRT statistic; consistency of large sample test; asymptotic power of large sample test.
  • Unit III:(Sequential Methods) Sequential tests: SPRT and its properties; Wald’s fundamental identity; OC and ASN functions; sequential estimation.
  • Unit IV:(Non-parametric Methods) Non-parametric methods: estimation and confidence interval; U-statistics and their asymptotic properties; UMVU estimator; nonparametric tests: single sample location, location-cum-symmetry, randomness and goodness of fit problems; rank order statistics; linear rank statistics; asymptotic relative efficiency.

Course Learning Objective

  1. Apply various parametric, non-parametric and sequential estimation techniques and testing procedures to deal with real life problems.
  2. Discuss the concept of consistency, CAN estimator and MLE.
  3. Discuss UMPU tests, SPRT, OC and ASN.
  4. Discuss the difference between UMP and UMP unbiased tests.
  5. Apply non-parametric methods and U-statistics.
  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. Gibbons, J. D. and Chakraborti, S. Nonparametric Statistical Inference. 4th ed. Marcel Dekker, 2003
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