Optimality

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Brief history of the Lehmann Symposia: Origins, goals and motivation The idea of the Lehmann Symposia as platforms to encourage a revival of interest in fundamental questions in theoretical statistics, while keeping in focus issues that arise in contemporary interdisciplinary cutting-edge scientific problems, developed during a conversation that I had with Victor Perez Abreu during one of my visits to Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. Our goal was and has been to showcase relevant theoretical work to encourage young researchers and students to engage in such work. The First Lehmann Symposium on <strong>Optimality</strong> took place in May of 2002 at Centro de Investigación en Matemáticas in Guanajuato, Mexico. A brief account of the Symposium has appeared in Vol. 44 of the Institute of Mathematical Statistics series of Lecture Notes and Monographs. The volume also contains several works presented during the First Lehmann Symposium. All papers were refereed. The program and a picture of the participants can be found on-line at the website http://www.stat.rice.edu/lehmann/lst-Lehmann.html. The Second Lehmann Symposium on <strong>Optimality</strong> was held from May 19–May 22, 2004 at Rice University. There were close to 175 participants in the Symposium. A partial list and a photograph of participants, as well as the details of the scientific program, are provided in the next few pages. All scientific activities took place in Duncan Hall in the School of Engineering. Most of the plenary and invited speakers agreed to be videotaped and their talks may be accessed by visiting the following website: http://webcast.rice.edu/webcast.php?action=details&event=408. All papers presented in this volume were refereed, and one third of submitted papers were rejected. At the time of this writing, plans are underway to hold the Third Lehmann Symposium at the Mathematical Sciences Research Institute during May of 2007. I want to acknowledge the help from members of the Scientific Program Committee: Jane-Ling Wang (UC Davis), David W. Scott (Rice University), Juliet P. Shaffer (UC Berkeley), Deborah Mayo (Virginia Polytechnic Institute), Jef Teugels (Katholieke Universiteit Leuven), James R. Thompson (Rice University), and Javier Rojo (Chair). The Symposia could not take place without generous financial support from various institutions. The First Symposium was financed in its entirety by CIMAT under the direction of Victor Perez Abreu. The Second Lehmann Symposium was generously funded by The National Science Foundation, Pfizer, Inc., The University of Texas MD Anderson Cancer Center, CIMAT, and Cytel. Shulamith Gross at NSF, Demissie Alemayehu at Pfizer, Gary Rosner at MD Anderson Cancer Center, Victor Perez Abreu at CIMAT, and Cyrrus Mehta at Cytel, encouraged and facilitated the process to obtain the support. The Rice University School of Engineering’s wonderful physical facilities were made available for the Symposium at no charge. v
vi Finally, thanks go the Statistics Department at Rice University for facilitating my participation in these activities. May 15th, 2006 Javier Rojo Rice University Editor
Page 1 and 2: Institute of Mathematical Statistic
Page 3 and 4: Institute of Mathematical Statistic
Page 5: iv Contents Copulas and Decoupling
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 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
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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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IMS Lecture Notes-Monograph Series
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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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