Optimality

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70 C. Cheng 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR Model 1 1 20 40 60 100 FDR control level in % q-value Model 3 1 20 40 60 100 FDR control level in % q-value Model 5 1 20 40 60 100 FDR control level in % q-value Model 7 1 20 40 60 100 FDR control level in % q-value Model 9 1 20 40 60 100 FDR control level in % q-value API Ip API Ip API Ip API Ip API Ip 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR 1 20 40 60 100 FDR control level in % BH AFDR Model 2 1 20 40 60 100 FDR control level in % q-value Model 4 1 20 40 60 100 FDR control level in % q-value Model 6 1 20 40 60 100 FDR control level in % q-value Model 8 1 20 40 60 100 FDR control level in % q-value Model 10 1 20 40 60 100 FDR control level in % q-value Fig 4. Simulation results on the rejection criteria. Each panel corresponds to a model configuration. Panels in the left column correspond to the “high noise” case σ = 3, and panels in the right column correspond to the “low noise” case σ = 1. The performance statistics �FDR (bullet) and � FNDP (diamond) are plotted against each criteria. Each panel has three sections. The left section shows FDR control with the Benjamini & Hochberg [3] adaptive procedure (BH AFDR), and the middle section shows FDR control by q-value, all at the 1%, 5%, 10%, 15%, 20%, 30%, 40%, 60%, and 70% levels. The right section shows �FDR and FNDP � of API and Ip. API Ip API Ip API Ip API Ip API Ip
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Model 1 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 3 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 5 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 7 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 9 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Massive multiple hypotheses testing 71 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Model 2 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 4 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 6 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 8 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Model 10 0.0 0.1 0.2 0.3 0.4 0.5 FDR^ 0.6 0.7 0.8 0.9 1.0 Fig 5. FNDP � vs. �FDR for Benjamini and Hochberg [3] adaptive FDR control (solid line and bullet) and q-value FDR control (dotted line and circle) when FDR control levels are set at 1%, 5%, 10%, 15%, 20%, 30%, 40%, 60%, and 70%. For each model FNDP � vs. �FDR of the adaptive API procedure occupies one point on the plot, indicated by a diamond.
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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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Page 41 and 42: power 0.02 0.03 0.04 0.05 0.06 0.07
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Page 47 and 48: Optimality in multiple testing 27 M
Page 49 and 50: 6. Summary Optimality in multiple t
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Page 53 and 54: IMS Lecture Notes-Monograph Series
Page 55 and 56: On the false discovery proportion 3
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Page 63 and 64: Since j≤ s, it follows that On th
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Page 73 and 74: Massive multiple hypotheses testing
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Page 85 and 86: Proof. See Appendix. Massive multip
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Page 93 and 94: Then π0α ∗ cal π0α ∗ cal +
Page 99 and 100: Frequentist statistics: theory of i
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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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