Statistics Qualifying Examination Syllabus

Probability Distributions: Standard distributions such as multinomial, Poisson, geometric, negative binomial, normal, gamma, beta, Weibull, multivariate normal; sampling distributions of statistics such as chi-squared, t, F distributions, order statistics; Student's Theorem; limit theorems.

Estimation: Confidence intervals; mean squared error. UMV unbiased estimates; maximum likelihood estimates; Cramer-Rao inequality; sufficiency and completeness; Rao-Blackwell and Lehmann-Scheffe theorems; applications to problems involving standard distributions; applications in linear models.

Hypotheses Testing: MP, UMP, and UMP unbiased tests; likelihood ratio tests; power of a test; efficiency of a test; applications to problems involving standard distributions; applications in linear models.

Other topics: Chi square tests; least squares; analysis of variance in one-way and two-way layouts; correlation and multiple regression.

Most of the material above can be found in:

•     Introduction to Mathematical Statistics by R. Hogg and A. Craig
•     Statistical Theory by B. Lindgren
•     Mathematical Statistics: basic ideas and selected topics by P.J. Bickel and K.A. Doksum
•     Mathematical Statistics and Data Analysis by John Rice
•     Linear Statistical Inference and Its Applications by C.R. Rao