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استنباط پیشرفته آماری 2

درساستنباط آماری پیشرفته ۲ به میزان چهار واحد درسی برای دانشجویان دکتری آمار با پیشنیاز استنباط آماری ۲ در نظر گرفته شده است.

 

ADVANCED STATISTICAL INFERENCE (II),

Second Term of 1397-1398

Contents:

Introduction to Statistical Hypotheses

Uniformly Most Powerful Tests (UMPT)

Uniformly Most Powerful and Unbiased Tests (UMPUT), Similar Tests,

Neyman Structure

Testing for Normal distribution

Locally (Unbiased) Most Powerful Tests (LMPT, ULMPT)

Invariance Testing

Minimax principle (Maximin Test, Locally Best Tests)

Conditional Inference (Mixtures)

(Generalized )Likelihood Ratio Tests (LRT, GLRT)

Some Important Results

Bayesian Analysis of Testing

Exam:

1) Mid Term exam (20 points)

2) Final Exam (50 points)

3) Seminar (+20 points)

4) Homework (up to +20 points)

References:

1) Lehmann, E. L. and Romono, J. P. (1986), Testing Statistical Hypotheses,

3rd ed., Springer: New York.

3) Ferguson, T. S. (1967), Mathematical Statistics, Academic Press: New

York

4) Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis,

2nd ed., Springer-Verlag: Berlin

5) Chao (2003), Mathematical Statistics, Springer, New York.

6) Casella, G. and Berger, R. L. (1990), Statistical Inference, Belmont:

7) Rohatgi, V. K. and Ehsanes Saleh, A. K. (2001), An Introduction to

Probability and Statistics, 2nd ed., John Wile: New York.

8) Roberts, C. R. (2007), The Bayesian Choice, Springer

9) Liese, F. and Miescke, K. J. (2008), Statistical Decision Theory, Springer

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