Asymptotic theory of testing statistical hypotheses : efficient statistics, optimality, power loss, and deficiency
著者
書誌事項
Asymptotic theory of testing statistical hypotheses : efficient statistics, optimality, power loss, and deficiency
（Modern probability and statistics）
VSP, 2000
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注記
Includes bibliographical references (p. 255-270) and index
内容説明・目次
内容説明
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
目次
- 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.
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