Asymptotic Theory of Testing Statistical Hypotheses

ASYMPTOTIC TEST THEORY: First-order asymptotic theory; Second order efficiency; On efficiency of first and second order; Power loss; Efficiency and deficiency; Deficiency results for the symmetry problems. ASYMPTOTIC EXPANSIONS UNDER ALTERNATIVES: Introduction; A formal rule; General Theorem; Proof of General Theorem; L-, R-, and U-statistics; Auxiliary lemmas. POWER LOSS: Introduction; General theorem; Tests based on L-, R-, and U-statistics; Proof of General Theorem - Lemmas; Proof of Lemmas; Power loss for L-, R-, and U-tests; Proof of Theorems; Combined L-tests; Other statistics. EDGEWORTH EXPANSION FOR THE LIKELIHOOD RATIO: Introduction; Moment conditions; case of independent but not identically distributed terms. A - LECAM'S THIRD LEMMA. B - CONVERGENCE RATE UNDER ALTERNATIVES: General theorem; Proof of Theorem B.1.1; L-, R-, and U-statistics; Proof of Theorem B.3.1. C - PROOF OF THEOREM 1.3.1. D - THE NEYMAN-PEARSON LEMMA. E - EDGEWORTH EXPANSIONS. F - PROOFS OF LEMMAS 2.6.1-2.6.5. G - PROOFS OF LEMMAS 3.7.1-3.7.5. H - ASYMPTOTICALLY COMPLETE CLASSES: Non-asymptotic theorem on complete classes; Asymptotic theorem on complete classes; Power functions of complete classes. I - HIGHER ORDER ASYMPTOTICS FOR R-, L-, AND U-STATISTICS: R-statistics; L-statistics; U-statistics; Symmetric statistics.