SUBJECT
Title
Statistical hypothesis testing
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Monotone likelihood ratio, testing hypotheses with one-sided alternative. Testing with two-sided alternatives in exponential families. Similar tests, Neyman structure. Hypothesis testing in presence of nuisance parameters.
Optimality of classical parametric tests. Asymptotic tests. The generalized likelihood ratio test. Chi-square tests.
Convergence of the empirical process to the Brownian bridge. Karhunen-Loève expansion of Gaussian processes. Asymptotic analysis of classical nonparametric tests.
Invariant and Bayes tests.
Connection between confidence sets and hypothesis testing.
Readings
E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.