B.Sc. Statistics
4th Semester Syllabus
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MJC-5 : Statistical Inference (सांख्यिकीय अनुमान)
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Unit 1: UNIT I
◦Estimation: Problem of estimation
◦Properties of a good estimator
◦Unbiasedness
◦Consistency
◦Efficiency and sufficiency
◦Factorization theorem
◦Cramer-Rao inequality and MVB estimators (statement and applications)
◦Minimum variance unbiased estimator (MVUE)
◦Rao-Blackwell theorem
Unit 2: UNIT II
◦Methods of Estimation: Method of moments
◦Method of maximum likelihood and minimum chi square
◦Properties of maximum likelihood estimators and minimum chi square (without proof)
Unit 3: UNIT III
◦Confidence interval: Confidence interval for mean
◦Proportion and variance
◦Bayesian Estimation: Loss function
◦Prior distribution
◦Bayes theorem
◦Posterior distributions
◦Bayes risk
◦Bayes principle
◦Bayes estimators
Unit 4: UNIT IV
◦Testing of hypothesis: Null and alternative hypotheses
◦Simple and composite hypotheses
◦Type-I and Type-II errors
◦Critical region
◦Level of significance
◦Size and power of a test
◦Best critical region
◦Most powerful test
◦Uniformly most powerful test
◦Neyman Pearson Lemma (statement and applications to construct most powerful test)
◦Likelihood ratio test
◦Properties of likelihood ratio tests (without proof)
Reference Books:
- Gupta, S. C. and Kapoor, V. K. (2020): Fundamentals of Mathematical Statistics, S. Chand & Sons, New Delhi.
- Goon A.M., Gupta M.K. and Dasgupta B. (2002): Fundamentals of Statistics, Vol. I & II, The World Press, Kolkata.
- Rohatgi V. K. and Saleh, A.K. Md. E (2009): An Introduction to Probability and Statistics, John Wiley and Sons.
- Mood A.M, Graybill F.A. and Boes D.C.: Introduction to the Theory of Statistics, McGraw Hill.