Statistics

Course Outline

Statistics

STATISTICS 

Estimation

  • Review of distribution and density functions, parametric families. Examples: binomial, Poisson, gamma. Sufficiency, minimal sufficiency, the Rao–Blackwell theorem. Maximum likelihood estimation. Confidence intervals. Use of prior distributions and Bayesian inference. [6]

Hypothesis testing

  • Simple examples of hypothesis testing, null and alternative hypothesis, critical region, size, power, type I and type II errors, Neyman–Pearson lemma. Significance level of outcome. Uniformly most powerful tests. Likelihood ratio, and use of generalised likelihood ratio to construct test statistics for composite hypotheses. Examples, including t-tests and F-tests. Relationship with confidence intervals. Goodnessof-fit tests and contingency tables. [4]

Linear models

  • Derivation and joint distribution of maximum likelihood estimators, least squares, Gauss-Markov theorem. Testing hypotheses, geometric interpretation. Examples, including simple linear regression and one-way analysis of variance. ∗Use of software∗. [6]

Appropriate books

  • D.A. Berry and B.W. Lindgren Statistics, Theory and Methods. Wadsworth 1995

  • G. Casella and J.O. Berger Statistical Inference. Duxbury 2001

  • M.H. DeGroot and M.J. Schervish Probability and Statistics. Pearson Education 2001