Syllabus  MA484/MA487
MA484/MA487 Statistics

Introduction to statistical inference: methods of estimation, least squares
and maximum likelihood, Bayes methods, properties of estimators

Approaches to statistics, including data analytic, frequentist, Bayesian,
robust, nonparametric, structural and fiducial. Ther role of probability
in the frequentist approach to statistical inference.

Brief review of random variables and their distributions. Some methods
of point estimation needed in hypothesis tests, including maximum likelihood
and method of moments.

Hypothesis testing: likelihood ratio tests, Neymann Pearson theory. Exponential
families of distributions. Derivation of uniformly most powerful tests
when they exist.
Discussion of uniformly most powerful unbiased tests. Discussion of
uniformly most accurate, and uniformly most accurate unbiased confidence
sets. Applications.

Principles of data reduction, with particular emphasis on the concept of
sufficiency. The concept of completeness.

Point estimation: criteria and derivations. Methods of estimation, especially
minimum variance unbiased estimators. Basu's Theorem. Applications.
Texts

R. Hogg & A. Craig, "Introduction to Mathematical Statistics" (Macmillan)
References

L.J. Bain & M. Engelhardt, "Introduction to Probability and Mathematical
Statistics" (van Nostrand Reinhold)

E.J. Dudewicz & S.N. Mishra, "Modern Mathematical Statistics" (Wiley)

P.G. Hoel, S.C. Port & C.J. Stone, "Introduction to Statistical Theory"
(Houghton Mifflin)

H.J. Larson, "Introduction to the Theory of Statistics" (Wiley)

A.M. Mood, F.A. Graybill & D.C. Boes, "Introduction to the Theory of
Statistics" (McGraw Hill)
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