Theory of Statistics I

Catalog description

Finite sample optimality of statistical procedures; Decision theory: loss, risk, admissibility; Principles of data reduction: sufficiency, ancillarity, completeness; Statistical models: exponential families, group families, nonparametric families; Point estimation: optimal unbiased and equivariant estimation, Bayes estimation, minimax estimation; Hypothesis testing and confidence intervals: uniformly most powerful tests, uniformly most accurate confidence intervals, optimal unbiased and invariant tests.