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Efron B., Tibshirani R. — An introduction to bootstrap |
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Предметный указатель |
- Bias-corrected accelerated, definition 185 401
- Bias-corrected accelerated, non-monotonicity 200
- Bias-corrected accelerated, percentile interval 178—201 216—217
statistic 242
ABC (approximate bootstrap confidence) intervals 188 328 378 400 401
Abramovitch, L. 335 413
Acceleration constant in one-parameter models 327
Acceleration constant, definition 186
Acceleration constant, two sample version 216
Accuracy of a confidence point 187 321
Adaptive estimation 258—270
Adjusted residual sum of squares 242
AIC- (Akaike's Information Criterion) 242
Akaike's information criterion (AIC) 242
Akaike, H. 255 413
Algorithm, bootstrap calibration 265
Algorithm, bootstrap hypothesis testing 221 224 232
Algorithm, bootstrap sampling 47
Algorithm, least median of squares regression 122
Algorithm, permutation test 208
Algorithm, variance stabilized bootstrap-t confidence point 164
Allen, D.M. 255 413
Anderson, T.W. 81 413
Antithetic sampling 356
Applications, aspirin 2—6
Applications, bioequivalence 126 372—391
Applications, cell survival 115—116
Applications, compliance (cholostyramine) 72
Applications, duodenal ulcer 243—247
Applications, hormone patch 127
Applications, law school 19
Applications, lutenizing hormone 92
Applications, mouse 11
Applications, spatial test 180
Applications, stamp thicknesses 227—233
Applications, test score data 62 143
Applications, tooth strengths 191
Approximate bootstrap, confidence (ABC) interval 188 328 378 400 401
Approximate bootstrap, quadratic ABC 333
Approximate likelihoods 358—371
Approximate pivot methods 362
Aspirin study 2—6
Assessing the error in bootstrap estimates 271—282
Asymptotic behavior of confidence points 187 321
Asymptotic result 154
Auto-regressive time series model 92—98
Automatic variance stabilization 163—166
Bai, C. 389 391 413
Balanced resampling 348
Barnard, G.A. 233 413
Barndorff-Neilson, O.E. 299 413
Baron Munchausen 5
Bayesian bootstrap 395
Bayesian information criterion (BIC) 242
Becker, R. 399 413
Beckman, R.M. 356 421
Behrens, B.-U. 234 413
Beran, R. 56 81 233 269 335 413 414
Bernoulli distribution 29
Besag, J. 234 414
Bias 124—140 142—153
Bias, bootstrap estimate of 124—132
Bias, correction 138
Bias, definition 124
Bias, infinitesimal jackknife estimate of 293
Bias, jackknife estimate of 133 141—152
Bias-corrected accelerated definition 185 401
Bias-corrected accelerated non-monotonicity 200
Bias-corrected accelerated percentile interval () 178—201 216—217
Bibby, J.M. 61 62 81 420
BIC- (Bayesian Information Criterion) 242
Bickel, P.J. 121 335 389 391 397 413 414
Binomial distribution 16 22 41—42
Bioequivalence 126 372—391
Bivariate normal distribution 54 58 181—182 377
Boos, D. 371 414
Bootstrap 46
Bootstrap "table" 159—160
Bootstrap, algorithm 47
Bootstrap, estimate of standard error 45—48
Bootstrap, hypothesis test 220—236
Bootstrap, ideal estimate 46 49
Bootstrap, nonparametric 47
Bootstrap, number of replications B 50—53 271 282
Bootstrap, origin of name 5
Bootstrap, parametric 48 53—55 306
Bootstrap, partial likelihood 364
Bootstrap, relationship with jackknife, infinitesimal jackknife, delta method 145—148 283—295 307—320
Bootstrap, replication 13 46 50—53
Bootstrap, sample 45
Bootstrap, sample size 51—52 271—282
Bootstrap, sampling 45
Bootstrap, schematic picture of 87 91 138
Bootstrap, simple description of 5 12—15
Bootstrap, smooth 231
Bootstraps interval 160—167
Bowman, A. 268 419
Box, G.E. 101 414
Boxplot 70
Breiman, L. 244 255 257 414
Bruce, P. 56 423
Buckland, S.T. 335 414
Buja, A. xv 319
Calibration, of a confidence point 263—270 334 388
Carlstein, E. 103 414
CART (Classification and regression tree) method 243—246 257
Central limit theorem 40
Chambers, J. 399 413 414
Chatfield, C. 102 414
Classification and regression tree (CART) method 243—246 257
Classification problem 236
Cleveland, W.S. 81 414
Clifford, P. 234 414
Cochran, W.G. 389 423
Coefficient of variation 44 52 273
Comparison of models 190—201 242—243
Complicated data structures 86—104
Components of variance 271—271
Computer programs 398—412
Confidence band for curve 268
Confidence interval, ABC 188 328 378 400 401
Confidence interval, accuracy 321
Confidence interval, bias-corrected accelerated () 185 178—201 216—217 402
Confidence interval, bootstrap-t 160 324
Confidence interval, correctness 322
Confidence interval, coverage 154
Confidence interval, definition 154
Confidence interval, equal-tailed 156
Confidence interval, length 180
Confidence interval, percentile 170 168—177
Confidence interval, quadratic ABC 333
Confidence interval, relationship with hypothesis testing 156—159 214—218
Confidence interval, shape 180
Confidence interval, standard normal 154 168
Confidence interval, Student's t 158—159
Conover, W.J. 356 421
Control functions 340
Correction for skewness 326—327
Correctness of a confidence point 322
Correlated data 92—104
Correlation coefficient 34 49—51 54—55
Covariance matrix 61 63
Coverage accuracy 187 321
Coverage error 322
Cox, D.R. 234 299 319 369 395 413 414 415
Crawford, S. 255 415
Cross-validation, generalized 255
Cross-validation, k-fold 239—241
Cross-validation, leave-one out 239—241
Cubic smoothing spline 259—260
| Curvature 330
Curve fitting 70—80 259—260
Davison A.C. xv 356 366 371 397 415
DeCleve, K. xv
Delete-d jackknife 149
Delta method 313—315
Density estimation 227 232 363 365
Density function 296
Dependence 396
Design matrix 106
Devroye, L. 57 415
Diaconis, P. 56 415
DiCiccio, T.J. 234 269 324 335 371 397 415 418
Diggle, P. 92 102 415
Directional data 397
Discrete distribution 24
Distribution function 22 296
Distribution function, nonparametric maximum likelihood estimate of 310
Distribution, Bernoulli 29
Distribution, binomial 22
Distribution, Gaussian (normal) 24—25 54 58 377
Distribution, Poisson 83
Do, K.A. 356 415
Double-blind study 2
Draper, N. 121 415
Ducharme, G. 56 81 397 413 415
Duodenal ulcer 243—247
Edgington, E.S. 218 415
Efficient computation of bootstrap estimates 338—357
Efron, B. 56 81 103 121 139 174 185 255 281 295 319 320 335 356 371 389 395 397 398 415 416
Eigenvalues of a matrix 63
Eigenvectors of a matrix 63
Empirical distribution function 32
Empirical distribution function as nonparametric maximim likelihood estimate 310
Empirical exponential family 318
Empirical likelihood 360
Equal-tailed confidence interval 156
Error rate estimation 237—255
Error, coverage 324
Error, prediction 237—257
Error, standard 11 39—44
Estimate 35
Estimating equation 397
Eubank, R.L. 81 268 417
Expectation 25
Exponential family model 316
Exponential model 304 313
Exponentially tilted distribution 235 353
Failure of the bootstrap 81
Faraway, J. 269 417
Feldman, D. 80 416
Fernholz, L.T. 319 417
Feucrverger, A. 397 417
Fieller's problem (ratio of means) 126—130 384—389
First-order accuracy 187 321
First-order correctness 187 321
Fisher information 305 307—308
Fisher's z-transformation 54 162
Fisher, N.I. 233 397 417
Fisher, R. 173 202 392
Frankel, M.R. 396 420
Freedman, D.A. 86 121 335 397 414 417 421
frequencies 22
Friedman, J. 244 414
Functional (plug-in) statistic 35 298
Gardner, M.L. xv
Gaussian (normal) model 24—25 54 58 377
GCV (Generalized cross validation) 255
Generalized Cross-Validation (GCV) 255
Geometric representation of the bootstrap and jackknife 283—295
Giampaolo, C. 243 255 417
Gine, E. 335 417
Gleason, J.R. 356 417
Glinos, T. xv
Godambe, V.P. 397 417
Golub, G. 63 255 417
Gong, G. 56 416
Graham, R.L. 356 417
Gray, A. 417
Gray, H.L. 150 417
Gross, S. 397 416
Group labels 206
Haerdle, W. 81 268 418 419
Hall, P. xv 56 81 233 234 268 269 281 324 325 335 356 357 371 397 415 417 418 419
Hammersley, J.M. 356 418
Hampel, F.R. 319 396 418
Handscomb, D.C. 356 418
Hartigan, J.A. 56 335 419
Hastie, T.J. xv 81 255 268 269 414 419 450
Hat matrix 255
Heart attacks 2
Heath, M. 255 417
Hesterberg, T. xv 356 419
Hinkley, D.V. 56 150 233 234 319 335 356 371 397 414 415 417 419
Hope, A.C.A. 56 233 419
Huber, P.J. 319 419
Hyperplane 288
Hypothesis testing 156—159 202—219 220—236
Hypothesis testing, one-sample 224
Hypothesis testing, relationship with confidence intervals 156—159 214—218
Hypothesis testing, two-sample 202 220
i.i.d. (independent and identically distributed) 9 28
Ideal bootstrap estimate 46 49 251
Implied likelihood 367—370
Implied prior distribution 367
Importance sampling 349—352
Improved estimate of bias 130—133 342—346
Independence 26
Indicator function 9 26
Infinitesimal jackknife 290 293 301
Infinitesimal jackknife, relationship with bootstrap, delta method 290 292 307 315
Influence, components 299
Influence, empirical 290
Influence, function 299
Information, Fisher (expected) 305 307—308
Information, observed 305 307—308
Izenman, A.J. 234 419
Jackknife, delete-d 149
Jackknife, estimate of bias 133
Jackknife, estimate of variance (standard error) 136 141
Jackknife, failure of 148—149
Jackknife, influence values 142 216 290 300—301
Jackknife, positive 290 203—295 301
Jackknife, pseudo-values 145
Jackknife, relationship with bootstrap 145—148 287 307
Jackknife, replication 134 142
Jackknife-after-bootstrap 275—280
Jaeckel, L. 319 419
Jeffreys, H. 371 419
Jenkins, G.M. 102 414
Jhun, M. 269 415 417
John, P.W.M. 356 417
Johns, V. 354 356 419
Kendall, M.G. 281 420
Kent, J.T. 61 62 81 319 420
Kernel density estimation 227 363 365
Kiefer, J. 319 371 420
Kish, L. 396 420
Knuth, D. iv 398 420
Kolaczyk, E. 371 420
Konishi, S. 335 420
Krewski, D. 397 420
Kuensch, H. 103 420
Kullback — Leibler distance 235
kurtosis 52 280 324
La Scala, B. 371 418
Lagrange multiplier 235
Laird, N. 397 420
Lamport, L. iv 420
Lawless, J. 371 421
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