Optimality

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192 V. H. de la Peña, R. Ibragimov and S. Sharakhmetov Theorem 5.5. The identically distributed r.v.’s X1, . . . , Xn are exchangeable if and only if the functions gi1,...,ic in representations (2.1) and (2.2) satisfy the conditions gi1,...,ic(ξi1, . . . , ξic) = gi π(1),...,i π(c) (ξi π(1) , . . . , ξi π(ic) ) (a.s.) for all 1≤i1
Copulas, information, dependence and decoupling 193 r.v.’s obtained by Wang [77]: For k = 0, 1,2, . . ., n� � F(x1, . . . , xn) = Fi(xi) 1 + i=1 � α1...αn (F αi1...αir+1 1≤i1
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Institute of Mathematical Statistic
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Institute of Mathematical Statistic
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iv Contents Copulas and Decoupling
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vi Finally, thanks go the Statistic
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SCIENTIFIC PROGRAM The Second Erich
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x Recent Advances in Longitudinal D
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The Second Lehmann Symposium—Opti
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xiv Richard Davis Colorado State Un
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xvi Matthias Matheas Rice Universit
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xviii Hui Zhao University of Texas
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IMS Lecture Notes-Monograph Series
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Proof. The maximum LR test rejects
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4. Location-scale families On likel
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6. Conclusions On likelihood ratio
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Student’s t-test for scale mixtur
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Optimality in multiple testing 17 w
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Optimality in multiple testing 19 I
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power 0.02 0.03 0.04 0.05 0.06 0.07
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Optimality in multiple testing 23 i
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Optimality in multiple testing 25 (
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Optimality in multiple testing 27 M
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6. Summary Optimality in multiple t
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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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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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Page 161 and 162: Semiparametric transformation model
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Page 197 and 198: Cumulative Hazard 0.0 0.2 0.4 0.6 0
Page 199 and 200: Hazard function 0.0 0.5 1.0 1.5 2.0
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Page 205 and 206: Copulas, information, dependence an
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Page 231 and 232: Regression trees 211 right model in
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Page 235 and 236: Regression trees 215 of the tree. T
Page 237 and 238: Regression trees 217 GUIDE methods
Page 239 and 240: Regression trees 219 and E appear a
Page 241 and 242: Regression trees 221 Table 3 Result
Page 243 and 244: Solder =thick 2.5 Regression trees
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Page 247 and 248: Regression trees 227 effects and in
Page 251 and 252: 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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