Optimality

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Institute of Mathematical Statistics LECTURE NOTES–MONOGRAPH SERIES Volume 49 <strong>Optimality</strong> The Second Erich L. Lehmann Symposium Javier Rojo, Editor Institute of Mathematical Statistics Beachwood, Ohio, USA
Institute of Mathematical Statistics Lecture Notes–Monograph Series Series Editor: Richard A. Vitale The production of the Institute of Mathematical Statistics Lecture Notes–Monograph Series is managed by the IMS Office: Jiayang Sun, Treasurer and Elyse Gustafson, Executive Director. Library of Congress Control Number: 2006929652 International Standard Book Number 0-940600-66-9 International Standard Serial Number 0749-2170 Copyright c○ 2006 Institute of Mathematical Statistics All rights reserved Printed in the United States of America
Page 1: Institute of Mathematical Statistic
Page 5 and 6: iv Contents Copulas and Decoupling
Page 7 and 8: vi Finally, thanks go the Statistic
Page 9 and 10: SCIENTIFIC PROGRAM The Second Erich
Page 11 and 12: x Recent Advances in Longitudinal D
Page 13 and 14: The Second Lehmann Symposium—Opti
Page 15 and 16: xiv Richard Davis Colorado State Un
Page 17 and 18: xvi Matthias Matheas Rice Universit
Page 19 and 20: xviii Hui Zhao University of Texas
Page 21 and 22: IMS Lecture Notes-Monograph Series
Page 23 and 24: Proof. The maximum LR test rejects
Page 25 and 26: 4. Location-scale families On likel
Page 27 and 28: 6. Conclusions On likelihood ratio
Page 29 and 30: IMS Lecture Notes-Monograph Series
Page 31 and 32: Student’s t-test for scale mixtur
Page 37 and 38: Optimality in multiple testing 17 w
Page 39 and 40: Optimality in multiple testing 19 I
Page 41 and 42: power 0.02 0.03 0.04 0.05 0.06 0.07
Page 43 and 44: Optimality in multiple testing 23 i
Page 45 and 46: Optimality in multiple testing 25 (
Page 47 and 48: Optimality in multiple testing 27 M
Page 49 and 50: 6. Summary Optimality in multiple t
Page 51 and 52: Optimality in multiple testing 31 [
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IMS Lecture Notes-Monograph Series
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On the false discovery proportion 3
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≤ N� � N� P m=1 On the fals
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Since j≤ s, it follows that On th
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0.025 0.02 0.015 0.01 0.005 On the
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Massive multiple hypotheses testing
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P value EDF qdf 0.0 0.2 0.4 0.6 0.8
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Proof. See Appendix. Massive multip
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X1 Massive multiple hypotheses test
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0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4
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Then π0α ∗ cal π0α ∗ cal +
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Frequentist statistics: theory of i
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2.3. Failure and confirmation Frequ
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3.1. Types of null hypothesis Frequ
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together with the probabilistic ass
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Statistical models: problem of spec
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Modeling inequality, spread in mult
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Semiparametric transformation model
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2.1. The model Semiparametric trans
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6.3. Part (ii) Put (6.1) (6.2) ˙Γ
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8. Proof of Proposition 2.3 Semipar
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Bayesian transformation hazard mode
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Cumulative Hazard 0.0 0.2 0.4 0.6 0
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Hazard function 0.0 0.5 1.0 1.5 2.0
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Copulas, information, dependence an
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Regression trees 211 right model in
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Abs(effects) 0.00 0.05 0.10 0.15 0.
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Regression trees 215 of the tree. T
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Regression trees 217 GUIDE methods
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Regression trees 219 and E appear a
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Regression trees 221 Table 3 Result
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Solder =thick 2.5 Regression trees
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Observed values 0 10 20 30 40 50 60
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Regression trees 227 effects and in
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On Competing risk and degradation p
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Restricted estimation in competing
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9. Conclusion 0.0 0.1 0.2 0.3 0.4 0
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2.1. Maximin efficiency robust test
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Robust tests for genetic associatio
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1 . . . 1 i . . . . . . R j . . . O
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Optimal sampling strategies 269 as
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Optimal sampling strategies 271 γ1
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Optimal sampling strategies 273 Def
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Optimal sampling strategies 275 Usi
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Optimal sampling strategies 277 Def
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optimal 1 2 3 4 leaf sets 5 6 (leaf
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6. Related work Optimal sampling st
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Optimal sampling strategies 283 Cla
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Optimal sampling strategies 285 Sin
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Optimal sampling strategies 287 µ
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Optimal sampling strategies 289 on
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Linear prediction after model selec
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y the P× 1 vector (3.1) ηn(p) = L
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Appendix B: Proofs for Section 5 Li
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Local asymptotic minimax risk/asymm
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Then (3.5) Local asymptotic minimax
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Moment-density estimation 323 may n
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3. The bias and MSE of ˆf ∗ α M
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Moment-density estimation 327 Corol
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Moment-density estimation 329 Suppo
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6. Simulations Moment-density estim
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Moment-density estimation 333 [7] M
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for positive α, and for α = 0 as
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Asymptotics of the MDPDE 337 Lemma
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Asymptotics of the MDPDE 339 asympt
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Optimality

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