Optimality

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200 V. H. de la Peña, R. Ibragimov and S. Sharakhmetov are equivalent. Taking ai1,...,ic = gi1,...,ic(xi1, . . . , xic), bi1,...,ic = dF(xi1, . . . , xic)/ � c j=1 dFij−1, for 1≤i1
Copulas, information, dependence and decoupling 201 R.v’s with the joint distribution function (8.6) are independent. Let now X1, . . . , Xn be independent r.v.’s with one-dimensional distribution functions Fi(xi), i = 1, . . . , n. Then their joint distribution function has form (8.6). This and the uniqueness of the functions gi1,...,ic given by Theorem 2.1 completes the proof of the theorem. Proof of Theorems 5.2–5.8. Below, we give proofs of Theorems 5.7 and 5.8. The rest of the theorems can be proven in a similar way. Let X1, . . . , Xn be r.v.’s with the joint distribution function satisfying representation (2.2) with functions gi1,...,ic such that Eξ αi 1 i1 ···ξ αic ic gi1,...,ic(ξi1, . . . , ξic) = 0, 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 169 and 170: 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
Page 203 and 204: IMS Lecture Notes-Monograph Series
Page 205 and 206: Copulas, information, dependence an
Page 219: Copulas, information, dependence an
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
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Page 239 and 240: Regression trees 219 and E appear a
Page 241 and 242: Regression trees 221 Table 3 Result
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Page 247 and 248: Regression trees 227 effects and in
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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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