Optimality

More documents

Recommendations

Info

332 R. M. Mnatsakanov and F. H. Ruymgaart ) x ( S 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 0 5 10 15 20 Fig 2. Figure 2. h = n −1/5 , respectively. To construct the graphs for the moment-type estimator ˆSα defined by (5.4) and the kernel-type estimator Sh defined in a similar way as the one given by (6.1) let us generate n = 400 copies of r.v.’s Y1, . . . , Yn with pdf g from (5.1) with W = 4 and x − 1−F(x) = e 2 + x x e− 2 , x≥0 . 2 We generated Y1, . . . , Yn as a mixture of two gamma G(1,2) and G(2, 2) distributions with equal proportions. In the Figure 2 the solid line represents the graph of S = 1−F while the dashed and dotted lines correspond to ˆ Sα and Sh, respectively. Here again we have α = n 2/5 and h = n −1/5 . References [1] Bhattacharyya, B. B., Kazempour, M. K. and Richardson, G. D. (1991). Length biased density estimation of fibres. J. Nonparametr. Statist. 1, 127–141. [2] Cox, D.R. (1969). Some sampling problems in technology. In New Developments in Survey Sampling (Johnson, N.L. and Smith, H. Jr., eds.). Wiley, New York, 506–527. [3] Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Vol. II. Wiley, New York. [4] Jones, M. C. (1991). Kernel density estimation for length biased data. Biometrika 78, 511–519. [5] Mnatsakanov, R. and Ruymgaart, F. H. (2003). Some properties of moment-empirical cdf’s with application to some inverse estimation problems. Math. Meth. Stat. 12, 478–495. [6] Mnatsakanov, R. and Ruymgaart, F. H. (2004). Some properties of moment-density estimators. Math. Meth. Statist., to appear.
Moment-density estimation 333 [7] Mnatsakanov, R. and Ruymgaart, F.H. (2005). Some results for momentempirical cumulative distribution functions. J. Nonparametr. Statist. 17, 733– 744. [8] Ross, S. M. (2003). Introduction to Probability Models. Acad. Press. [9] Vardi, Y. (1985). Empirical distributions in selection bias models (with discussion). Ann. Statist. 13, 178–205.
Page 1 and 2:
Institute of Mathematical Statistic
Page 3 and 4:
Institute of Mathematical Statistic
Page 5 and 6:
iv Contents Copulas and Decoupling
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 29 and 30:
Page 31 and 32:
Student’s t-test for scale mixtur
Page 33 and 34:
Page 35 and 36:
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 [
Page 53 and 54:
Page 55 and 56:
On the false discovery proportion 3
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
≤ N� � N� P m=1 On the fals
Page 63 and 64:
Since j≤ s, it follows that On th
Page 65 and 66:
0.025 0.02 0.015 0.01 0.005 On the
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Massive multiple hypotheses testing
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
P value EDF qdf 0.0 0.2 0.4 0.6 0.8
Page 83 and 84:
Page 85 and 86:
Proof. See Appendix. Massive multip
Page 87 and 88:
X1 Massive multiple hypotheses test
Page 89 and 90:
Page 91 and 92:
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4
Page 93 and 94:
Then π0α ∗ cal π0α ∗ cal +
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Frequentist statistics: theory of i
Page 101 and 102:
Page 103 and 104:
2.3. Failure and confirmation Frequ
Page 105 and 106:
3.1. Types of null hypothesis Frequ
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
together with the probabilistic ass
Page 121 and 122:
Statistical models: problem of spec
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Modeling inequality, spread in mult
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Semiparametric transformation model
Page 155 and 156:
2.1. The model Semiparametric trans
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
6.3. Part (ii) Put (6.1) (6.2) ˙Γ
Page 181 and 182:
Page 183 and 184:
8. Proof of Proposition 2.3 Semipar
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Bayesian transformation hazard mode
Page 193 and 194:
Page 195 and 196:
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 201 and 202:
Page 203 and 204:
Page 205 and 206:
Copulas, information, dependence an
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Regression trees 211 right model in
Page 233 and 234:
Abs(effects) 0.00 0.05 0.10 0.15 0.
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
Page 245 and 246:
Observed values 0 10 20 30 40 50 60
Page 247 and 248:
Regression trees 227 effects and in
Page 249 and 250:
Page 251 and 252:
On Competing risk and degradation p
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Restricted estimation in competing
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
9. Conclusion 0.0 0.1 0.2 0.3 0.4 0
Page 273 and 274:
Page 275 and 276:
2.1. Maximin efficiency robust test
Page 277 and 278:
Robust tests for genetic associatio
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
1 . . . 1 i . . . . . . R j . . . O
Page 289 and 290:
Optimal sampling strategies 269 as
Page 291 and 292:
Optimal sampling strategies 271 γ1
Page 293 and 294:
Optimal sampling strategies 273 Def
Page 295 and 296:
Optimal sampling strategies 275 Usi
Page 297 and 298:
Optimal sampling strategies 277 Def
Page 299 and 300:
optimal 1 2 3 4 leaf sets 5 6 (leaf
Page 301 and 302: 6. Related work Optimal sampling st
Page 303 and 304: Optimal sampling strategies 283 Cla
Page 305 and 306: Optimal sampling strategies 285 Sin
Page 307 and 308: Optimal sampling strategies 287 µ
Page 309 and 310: Optimal sampling strategies 289 on
Page 311 and 312: IMS Lecture Notes-Monograph Series
Page 313 and 314: Linear prediction after model selec
Page 315 and 316: y the P× 1 vector (3.1) ηn(p) = L
Page 329 and 330: Appendix B: Proofs for Section 5 Li
Page 333 and 334: Local asymptotic minimax risk/asymm
Page 337 and 338: Then (3.5) Local asymptotic minimax
Page 343 and 344: Moment-density estimation 323 may n
Page 345 and 346: 3. The bias and MSE of ˆf ∗ α M
Page 347 and 348: Moment-density estimation 327 Corol
Page 349 and 350: Moment-density estimation 329 Suppo
Page 351: 6. Simulations Moment-density estim
Page 355 and 356: for positive α, and for α = 0 as
Page 357 and 358: Asymptotics of the MDPDE 337 Lemma
Page 359: Asymptotics of the MDPDE 339 asympt
show all

Optimality

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?