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Gruber M.H.J. — Regression Estimators: A Comparative Study |
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Предметный указатель |
"half Kalman Filter" 224
Additional observations 10 69 79 82 106 120 171 296
Admissible estimator 17 21 50 53—55 145 146
Akdeniz, E. 26
Akdeniz, F. 23 25 26 28
Albert, A. 48
Alheety, M.I. 28
Ali, M.A. 17
Alternative forms of the Bayes estimator 95—100 103 116 117—129 130 131 133
Alternative forms of the mixed estimator 103—109
Alternative forms of the MSE 153—157 167
Amari, S. 19 355
Analysis of variance (Anova) 10 31 35 252—262 288 298
Analysis of variance (ANOVA), one-way classification 252 253 253—263 278
Analysis of variance (ANOVA), two-way classification 252 267—273 277 278
Andrews, A.P. 19
Applications, aerospace tracking 223 224
Applications, analysis of life lengths 223
Applications, design of experiments 252 270 272 277
Applications, dose-response experiment 223
Applications, Earth's magnetic field 245
Applications, gross national product 6
Applications, measurement process 246
Applications, navigation 19 244—248
Applications, satellite tracking 244 245
Applications, ship's motion 245—248
Applications, underwater sonar 223
Approximate Bayes estimator 253
Arsenin, V.Y. 11
Arslan, O. 23
Askin, R.G. 22 23
Asters, R.C. 11
Atkinson, C. 19 366 367
Augmented linear model 11 69 111 117 121 130 187 234 308 341 384
Average MSE 13 32 50 52 136 138
Average MSE of Bayes estimator 153—155
Average MSE of contraction estimator 162—164
Average MSE of empirical Bayes estimator 265 276 278—282
Average MSE of Kalman Filter 239—242
Average MSE of Liu estimator 165
Average risk averaging over LINEX loss function 333—340
Average risk averaging over squared error loss function 13 32 50 52 136 138 153—155 162—164 165 239—242 265 276 278—282
Average risk averaging over Zellner's balanced loss function 312—315
Average variance of BE 147 151—152
Baksalary, J.K. 18
Baldwin, K.F. 9 12 13 20 23 24 27
Bannerjee, K.S. 11
Basis for a vector space 15 273 278 357 358
Basis for spline model 285—287 289
Batah, F.M. 30
Baye, M.R. 21 30 110 116
Bayes estimator, admissibility of 53 145
Bayes estimator, alternative forms of 12 22 95—100
Bayes estimator, average MSE of 138 147—156 157—160 162—165 336—340
Bayes estimator, comparison with least square estimator 174—187
Bayes estimator, comparison with minimax estimator 56 296
Bayes estimator, comparison with mixed estimator 233—234 308
Bayes estimator, comparison with ridge-type estimator 101—111
Bayes estimator, conditional MSE of 168—171 174—187 192—193 201 315—318 340—352
Bayes estimator, distance between 354 369—384
Bayes estimator, extensions of BLUR 24
Bayes estimator, formulation of 12 26 27 31 34 48—53 88—92 263—264 273—275 306—307 333—336
Bayes estimator, iterated 225—228
Bayes estimator, linear 18 70 88—92 145 146
Bayes estimator, robustness of 203—208 214—240
Bayes estimator, special cases of 3 12 14 94 117—129 291—299
Bayes risk 26 56 138 143 144 146 174 333—339 352
Bayes theorem 34 48 49 227
Berger, J.O. 14 15 203
Berliner, M. 14 203
Best linear unbiased estimator (BLUE) 74 76
Best linear unbiased predictor (BLUP) 18 24 284 290—299
Bias 9 13 17 18 20 27—30 52 111 135 137—138 148 168—170 196—198 336 337
Biased estimator 13 26 30 111
Biased prior information 203 211
Biasing parameter 13 20 21 22 24 25 27 28 29 30
Billor, N. 23
Birkes, D. 19
Bock, M.E. 203
Borchers, B. 11
Bozdogan, H. 29
Brown, K.G. 12
Brown, R.G. 227
Bucy, R.S. 223
Bulmer, M.G. 292
Bunke, H. 15
Bunke, O. 15 20
Burbea, J. 19
Burr, T.L. 26
Camara, V.A.P. 27 325 326
Carr, R.N. 11
Carroll, R.J. 24 283 289 298
Cassella, G. 24
Catlin, D. 223
Cauchy — Schwarz inequality 60
Chang, X. 31
Change of coordinate 177
Characteristic equation 62 63
Chaubey, Y.P. 17 30
Chawla, J.S. 17
Clark, A.E. 29
Column space 41 104 121 122 124 125 273
Comparison of conditional and average MSE 179—181
Comparison of conditional MSE for a BE and an LS 174—179 181—187
Comparison of conditional MSE for ridge-type estimator and an LS 12 18 178 181
Comparison of conditional MSE for two BE 192—194
Comparison of ridge-type estimators and LS estimators under incorrect prior assumptions 202—220
Completely randomized design 252
Conditional expectation 52 336
Conditional MSE 32 135—137 167—201 202 209
Conditional MSE of Bayes estimator 52 139 214 215 218
Conditional MSE of least square estimator 148 218
Conditional MSE of ridge-type estimator 60 139
Conklin, W.M. 29
Constraint, exact 24—26 254 267
Constraint, linear 24 74
Constraint, quadratic 25 29 289 295
Constraint, stochastic prior 22 25 26 121 211 307 385—387
Contaminated Bayes estimators 217—228
Contaminated priors 213—217
Contraction estimators 12 162—164 179 194 195 197
contrast 254 256 261 269 278
Convex combinations 303 305 310 312
Convex loss function 333
Correct prior assumptions 137 139 202—205 207 209 211 212 242 243
Costa, S.I. 19
Craig, A. 143
Crivelli, A. 19
Crouse, R.H. 20 21 29
Dagnelie, P. 20
Daniel, C. 17
De Boer, P.M. 27
Decision function 56
Dempster, A.P. 9 12 13 154
Design matrix 10 11 20 22 34 94 129 174 245 252
Determinant 35 36 196 372
Dey, D. 26
Diderrich, G.T. 224
Differential equation 83
Differential equation for geodesic 362—363
Differential geometry 354 355—369 389
Differential geometry, affine connection 355 361
Differential geometry, Christoffel symbols 361
Differential geometry, covariant derivative 361—362
Differential geometry, geodesic 354 355 361 362 364—367 385 387—389
Differential geometry, manifold 354—357 359—362 389
Differential geometry, Riemannian metric 354 355 358—360 389
Differential geometry, tangent space 355 357—359 361 389
Discrete Kalman Filter 32 224
dispersion 4 30 143 155 161 205 214 251 340 354 367 376 381—389
| Dispersion of estimator 5 36
Dispersion of prior 14 101—103 117—120 157—159 163 165 174 179 185 193—195 197 248
Dispersion, conditional 196
Dispersion, initial 248
Dispersion, misspecified 202 203 242
Do Carmo, M.P. 355 362
Dodge, Y. 19
Druilhet, P. 30
Drygas, H. 21
Duncan, D.B. 11 95
Ebegil, M. 29
Efficiency of estimators 22 25 32 33 135 147—148 153 165 196 209 217 218 253 292—294
Efron, B. 253 267
Eigenvalue 26 61
Eigenvalue in distance functions 355 367 369 371 372 383 385
Eigenvalue in SVD 38—40 255
Eigenvalue of design matrix 5—7 10 107 108 268 343
Eigenvalue of positive semi-definite matrix 35—37 58
Eigenvalue of prior 209
Eigenvalue of shrinkage matrix 28
Eigenvector 58 61 255 268 367 369 376 379 389
Ekni, M. 29
Ellipsoid for comparing efficiency of estimators 167 174—193 201
Ellipsoid for incorrect prior assumptions 137 202—220
Ellipsoid for minimax estimators 14—16 20 22 26 30 35 56 86 136 147 208—210
Ellipsoid for ridge regression 6 10 76
Empirical Bayes estimator (EBE) 12 15 26 31 94 253 259 263—267 273—278
Epsilon contaminated prior distribution 14 214—217
Error of measurement 246
Estimable parametric functions for estimators 98—101 119 153—154 159 170 175 188 190—192 217 264 275
Estimable parametric functions for studying the efficiency of estimators 167 174—193 201
Estimable parametric functions, (X, R) estimable 81 84 105 136 149 151
Estimable parametric functions, definition and properties of 70—74 92 148 253—257 261 268—269 303 305 306 309 319
Estimable parametric functions, R estimable 81 104 149 157
Estimable parametric functions, X estimable 81 84 104 105 151 162
Eubank, R.L. 25 223
Exchangeability of sample and prior information 131
Experimental design models 4 32 252—282
Farebrother, R.L. 12 13 14 18 60 71 181
Ferguson, T.S. 56
Feynman, R.P. 135
Firinguetti, L. 17 19
Fixed effects model 253 271
Flack, V.F. 17
Foucart, T. 28
Frequentist argument 101 318
Fry, H. 26
Fu, W.J. 22
Gaffke, N. 18
Galarneau, D.I. 13 22
Gamma distribution 368
Gana, R. 20
Gauss — Markov theorem (GM) 11 15 69 74—76 81 89 94 116—117 130
Gauss — Markov theorem (GM), extended GM 96 98 116—117 130
Gauss — Markov theorem (GM), statement and proof of GM 74—75 90 116—117 130
Generalized inverse and least square estimators 70—76 80 81 256—268
Generalized inverse and parametric functions 254—255 305
Generalized inverse and the singular value decomposition 34 38
Generalized inverse, definition and properties of 5 32 41—48
Generalized ridge estimator 15 32 343
Generalized ridge estimator as a special case of a broader class of estimators 109—116 130
Generalized ridge estimator for LINEX loss function 342—351
Generalized ridge estimator for Zellner's balanced loss function 310—312 322
Generalized ridge estimator, comparison with least square estimator 14 17 20 22 178 342—351
Generalized ridge estimator, comparison with other ridge-type estimators 17 27 30 101—103 162 195
Generalized ridge estimator, derivation of 76—77 129—130 237—239
Generalized ridge estimator, examples of 77—79 102—103 113—115 180
Ghosh, H. 31
Gibbons, D.G. 13 28
Gokpinar, E. 29
Goldberger, A.S. 10 14 18
Goldstein, M. 11
Golub, G. 13
Gore, S.D. 28 30
Graybill, F.A. 48 64
Grewal, M.S. 19
Gross, J. 20 21 22 24 146
Gruber, M.H.J. 9 12 13 14 18 22 23 25 30 55 96 111 224 317 324
Gunst, R.F. 20
Hafner, C.M. 27
Haitovsky, Y. 13
Hald, A. 22 23
Hampel, F.R. 23
Hanumara, R.C. 20 29
Haq, W.S. 21
Harrison, C.F. 223
Harville, D.H. 11 95
Haughton, D.M.A. 29
Heath, M. 13
Heffes, H. 224
Heiligers, M.R. 18
Hemmerle, W.J. 27
Henderson, C.R. 18 24
Herring, F. 16
Heumann, B. 25
Higgens — Tsoskos loss function 340 351—353
Hocking, R.R. 24
Hoerl, A.E. 4 6 9 10 11 12 13 18 20 21 23 24 25 27 28 30 69 77 101 110 112 129 181 208 310 317 322 343 376 377 382 383
Hoerl, R.W. 11
Hogg, R.V. 143
Holzworth, R.J. 21
Horn, S.D. 11 95
Hu, H. 27
Huber, P.J. 23 29
Hubert, M.H. 28
Humak, K.M.S. 15
Ibrahim, M. 28
Iemma, A.F. 20
Inadmissible estimator 10 15 34 53—55 111 144 330
Incorrect, ellipsoid 137 220
Incorrect, prior information 14 28 32 136—140 201—220 242—244
Incorrect, prior mean 201—205 210 242
Increasing function 163 195 328 329 378 384
Independent linear models 140 303 304 324
Inference procedure 225 251
Information geometry 4 19 33 354—389
Information geometry, Fisher information 19 354 355 358—361 389
Information geometry, Rao distance 19 354 355 361 363—369 372—374 386 389
Initial prior dispersion 248
Initial prior information 234 239
Initial prior mean 225
Inner product 358 359
Inoue, T. 23
Iterative procedure 225 227
Iyengar, N.S. 14
Jack-knife estimator 16—18 30 171
James — Stein estimator 10 12 13 15 20 22 23 25 27 54 55 94 110
James, W. 10 12 13 15 20 22 23 25 27 54 55 94 110 111 140 219 251 259 265 275 277 278 322
Jin, C. 20 29
Judge, G. 203
Kaciranlar, M.R. 29 30 111
Kadiyala, K. 18 23
Kagan, L.M. 91
Kalman filter 4 18 19 32 95 223—251 354 355 387—389
Kalman gain 227 237
Kalman, R.E. 4 18 32 95 223 224 225 227 228 229 230 235 236 237 239 242 244 245 248 251 354 387 388
Kauermann, G. 289
Kennard, R.W. 4 6 9 10 11 12 13 18 20 21 23 24 25 27 28 30 69 77 101 110 112 129 181 208 310 317 322 343 376 377 382 383
Khalaf, G. 27
Kibria, B.M.G. 21 24 25 26 29
Kim, D. 31
Kim, D.H. 31
Kim, M. 31
Klintworth, M. 26
Knots 283 286—289 291 294
Kozak, J. 14
Kronecker product 33 63—65
Krzanowski, W.J. 19 368 376
Kubokawa, T. 26 27
Kuks, J. 20 22
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