Methods of estimation. Moments. Method of Maximum likelihood and Least squares. Ordered least squares estimation of location and scale parameters. Bayes method of estimation, minimum chi-square. Simple and composite hypothesis. Size and power of a test. Power function. Most powerful test. Neyman-Pearson lemma, critical regions Bayes test. Randomized test, unbiased tests. Likelihood ratio test. Uniformly most powerful test. Sequential probability ratio test, its properties. ASN and OC functions. Test for proportions and standard deviations. Confidence interval and its interpretation. One sided confidence intervals. Methods of finding confidence intervals. Bayesian interval estimates shortest sets of confidence intervals.

To familiarize students with construction of different types of Confidence Intervals, hypothesis testing procedures and sequential analysis.

• . Explain and apply approaches to our confidence in them by examining the area of interval estimation. • Asses the plausibility of pre-specified ideas about the parameters of a model by examining the area of hypothesis testing. • The understanding of the concepts of testing, size and power of a test. • The understanding of and derivation of simple and generalized likelihood ratio theory.

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Book Title : Introduction to Mathematical Statistics

Author : Hogg, R.V. and Graig A.T.

Edition : 7th

Publisher : Prentice-Hall International, Inc. Engle Wood Cliff, N.T.

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Book Title : Introduction to the Theory of Statistics

Author : Mood, A.M., Graybill, F.A. and Boes, D.C.

Edition : 3rd

Publisher : McGraw Hill Book Co., N.Y

Title : (5) Testing of Hypothesis 4- GLR test and UMP test

Type : Presentation

View (5) Testing of Hypothesis 4- GLR test and UMP test

Title : (6) Sequential Probability ratio test _ Average sample number

Type : Presentation

View (6) Sequential Probability ratio test _ Average sample number