Optimality

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Contents Preface: Brief history of the Lehmann Symposia: Origins, goals and motivation Javier Rojo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Contributors to this volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Scientific program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Partial list of participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Acknowledgement of referees’ services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix PAPERS Testing On likelihood ratio tests Erich L. Lehmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Student’s t-test for scale mixture errors Gábor J. Székely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Multiple Testing Recent developments towards optimality in multiple hypothesis testing Juliet Popper Shaffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 On stepdown control of the false discovery proportion Joseph P. Romano and Azeem M. Shaikh . . . . . . . . . . . . . . . . . . . . . . . . . 33 An adaptive significance threshold criterion for massive multiple hypotheses testing Cheng Cheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Philosophy Frequentist statistics as a theory of inductive inference Deborah G. Mayo and D. R. Cox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Where do statistical models come from? Revisiting the problem of specification Aris Spanos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Transformation Models, Proportional Hazards Modeling inequality and spread in multiple regression Rolf Aaberge, Steinar Bjerve and Kjell Doksum . . . . . . . . . . . . . . . . . . . . . . 120 Estimation in a class of semiparametric transformation models Dorota M. Dabrowska . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Bayesian transformation hazard models Gousheng Yin and Joseph G. Ibrahim . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 iii
iv Contents Copulas and Decoupling Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series Victor H. de la Peña, Rustam Ibragimov and Shaturgun Sharakhmetov . . . . . . . . . 183 Regression Trees Regression tree models for designed experiments Wei-Yin Loh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Competing Risks On competing risk and degradation processes Nozer D. Singpurwalla . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Restricted estimation of the cumulative incidence functions corresponding to competing risks Hammou El Barmi and Hari Mukerjee . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Robustness Comparison of robust tests for genetic association using case-control studies Gang Zheng, Boris Freidlin and Joseph L. Gastwirth . . . . . . . . . . . . . . . . . . . 253 Multiscale Stochastic Processes Optimal sampling strategies for multiscale stochastic processes Vinay J. Ribeiro, Rudolf H. Riedi and Richard G. Baraniuk . . . . . . . . . . . . . . . 266 Asymptotics The distribution of a linear predictor after model selection: Unconditional finitesample distributions and asymptotic approximations Hannes Leeb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal experiments under asymmetric loss Debasis Bhattacharya and A. K. Basu . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 Density Estimation On moment-density estimation in some biased models Robert M. Mnatsakanov and Frits H. Ruymgaart . . . . . . . . . . . . . . . . . . . . . 322 A note on the asymptotic distribution of the minimum density power divergence estimator Sergio F. Juárez and William R. Schucany . . . . . . . . . . . . . . . . . . . . . . . . 334
Page 1 and 2: Institute of Mathematical Statistic
Page 3: Institute of Mathematical Statistic
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 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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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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