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Takezawa K. — Introduction to Nonparametric Regression
Takezawa K. — Introduction to Nonparametric Regression



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Название: Introduction to Nonparametric Regression

Автор: Takezawa K.

Аннотация:

Written for undergraduate and graduate courses, this text takes a step-by-step approach and assumes students have only a basic knowledge of linear algebra and statistics. The explanations therefore avoid complex mathematics and excessive abstract theory, and even statistical information is accompanied by clear numerical examples and equations are explained all the way through the process. Topics include smoothing out data with an equispaced predictor, nonparametric regression for a one-dimensional predictor, multidimensional smoothing, nonparametric regression with predictors represented as distributions, smoothing of histograms and nonparametric probability density functions and pattern recognition. Each chapter includes exercises.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 568

Добавлена в каталог: 18.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Method of Lagrange multipliers (Lagrange multiplier method)      242 441
Midrange      191 222
Misclassification      412
Misclassification rate      418 427 428 463 471
MODE      9 10
Model      2
Model error      2
Model matrix      33
Modeling      1 2
moment      166 384
Moore — Penrose generalized inverse matrix      320
Moving Average      5 23 79 81 95 501 502
Multinomial distribution      365
Multinominal logistic regression      425
Multiple knot      479
Multiple regression      33 86
Multiple regression (multiple linear regression)      32 125 377
Multiple regression equation      35 275 283 330
Multiple regression equation (multiple linear regression equation)      482
Multiple root      75
Multiplication rule      130
Multiplication theorem      130
Nadaraya — Watson estimator      104 133 197 199 226 502
Names      204
Natural boundary conditions      159 227 480 489
Natural cubic spline      15 158 234
Natural link function (canonical link function)      373
Natural spline      158 208 394 473 479 488 503 526
Natural thin plate splines (natural thin plate spline)      234
Natural-spline basis      480
Nearest-neighbor local-linear regression      186
Neumann conditions      159
Neural networks      20 425 427 459 526
Newton — Raphson algorithm      373
Node      430
Nonlinear model      18
Nonlinear regression      18
Nonparametric DVR method (nonparametric Developmental Rate method)      335 343
Nonparametric probability density function      396 399 453 455 520 521 524
Nonparametric probability density function (nonparametric density function)      380 418
Nonparametric probability density function estimation (nonparametric density function estimation)      3
Nonparametric regression      1 24 103 231 325 359 409
Normal distribution      10 16 124 125 128 227 286 360 361 368 390 407 414 444 523
Normal equation      33 260 304 306 319 320 487 514
Normalization      146 177 189
Null space      349
Nullity      349
Ordinary Cross-Validation (OCV)      116
Ordinary kriging      243 252 297 319 510
Orthogonal coordinate system      58
Orthogonal matrix      56 144 145 181 251
Orthogonal projection      40 59 78
Orthogonal projection matrix      40 57
Orthogonal sum      443
Orthogonal system      260
Orthonormal polynomial      100
Outlier      195
Output argument      80 200 288 345 387
PARAMETER      13 18
Parameterization      19
Parametric function      19 103
Parametric probability density function estimation (parametric density function estimation)      3
Parametric regression      3 18
Partial spline      215 270 321
Parzen kernel      200
Pascal’s triangle      28
Pattern      410
Pattern recognition      409
Penalized regression      51
Penalty matrix      177 182
Periodic boundary condition      95
Perspective plot      82 302 304 317
Piecewise fitting      43
Poisson distribution      361—363 365 368 372 373 378 390 406 407 429
Poisson ratio      235
Poisson regression      372 390 422
Polynomial      32 85 87 96 111 112 128 502
Polynomial (polynomial function)      16 32 103 394 482 502
Polynomial regression      111 125 140
Population      410
Population mean      105
Positive definite matrix      251
Possible sunshine duration      335
Posterior probability      414
Power method      281 323
Predictand      2
Predictant      2
Prediction equation      2
Prediction error      115 191
Prediction Mean Squared Error (PMSE)      115
Predictor      2 23 103 231 325 359 483
Preprocessing      410
Principal component analysis      284 287 444
Principal component regression      284
Principle of minimum potential energy      168
Prior probability      414
Prior weight      373
Probability density function      2 121 125 130 229 339 341 362 421
Probability density function (density function)      114 360 410
Probit transformation      422 471
Projection      40 57 286
Projection index      287
Projection matrix      40 56
Projection pursuit      286
Projection pursuit regression      284 315 515
Projection-type smoother      260
Prospective view      116
Pruning      431
QR decomposition      179 251
Quadratic discriminant rule      418 448 451 453 471 524
Quadratic equation      38
Quadratic form      483
Quasi-definite matrix      181
Quasi-definite matrix (positive semidefinite matrix, nonnegative definite matrix)      67 144 281 330
Quasi-likelihood      390
Random variable      130 239 413 421
RBF (Radial Basis Function)      344
Realization      2 16 110 234 263 341 406 407 471
Reflection boundary condition      24 95 98
Reflective boundary condition      55
Regressand      2
Regressing      2
Regression      1 103
Regression analysis      325 409
Regression coefficient      18 34 35 47 49 50 99 111 239 330 332 349 350 359 437 480
Regression equation      16 18 245
Regression equation (regression function)      2 32 104 235 326 359
Regression model      2
Regressor      2
Regressor variable      2
Regular matrix      56 175 240 243
Regularization parameter      427
Residual      40
Residual sum of squares      33 285 286 359 361 376 429 438
Residual sum of squares (RSS)      116
Response variable (response)      2
Retrospective view      116
Ridge regression      330
Robust version of LOESS      195 223 229 506
Robustness weight      195
Roughness penalty      51 170 174 177 181 182 185 215 341 343 483
Sample      16 105 410
Sample mean      416
Sample variance      416
Sampling      410
Sampling distribution      105
Saturated model      367
Scale estimate      197
Scaled deviance      368
Schoenberg — Whitney conditions      158 482
Schoenberg — Whitney theorem      158
Second derivative function      152 479
Semi-variogram      244
Semiparametric regression      270
Shearing force diagram      167
Sherman — Morrison — Woodbury theorem      226
Simple kriging      245 252 298 299 319 511
Simple regression      275 377
Simple regression equation      275
Simply supported beam      166
Sine wave      5
Singular value decomposition      179
Smoothing      103 235 335 360
Smoothing matrix      40
Smoothing matrix (smoother matrix)      32
Smoothing parameter      51 55 121 144 170 191 209 235 307 319 329 331 332 339 341 349 504
Smoothing spline      91 98 99 118 156 170 172 177—179 181 184 209 216 226 237 266 269 270 341 504
Smoothing spline (smoothing splines)      7 51 104 236 329 378 394 473 502
Softmax function      425 427 460
span      186 227 270
Spectral resolution (spectral decomposition)      56
Spectrum      56
Spherical correlogram      245
SPLINE      43 152
Spline basis      474 480
Spline Function      43 88 152 473 502
Splitting rule      430
Spring constant      167
Standard deviation      10 243
Statistics      116
Sturges’ rule      9
SubMatrix      176
subspace      444
Supersmoother      104 191 221 228 281 285 314 506 515
Supervised learning      410
Support      474
Symmetric matrix      40 55 98 144 240 323 417 441
Target variable (object variable)      2 23 107 239 325 359 437 490
Taylor expansion      39 139 151 233 372
Terminal node      429 461
Test data      413
Theoretical correlogram      252 256 298 302 303 319
Theoretical correlogram (correlogram model)      245 301 512
Theoretical variogram      252 304
Theoretical variogram (variogram model)      245
Thin plate smoothing spline      235
Thin plate smoothing splines      236 252 256 291 438 507 508
Thin plate splines (thin plate spline)      234 235 237
Third derivative function      152
Time-series data      23
Total covariance      439
Total variability      41
Trace      124
Trade-off      51
Trade-off of bias versus variance (bias-variance trade-off)      107 178 226
Training data      413
TRANSPOSE      33 111
Tree-based model      429 460 471 526
Tricube weight function      140 186 237
Trimodal      9
Triweight      140
Truncated power function      151 482
Tweeter      191 222
Unbiased      125
Unbiased estimator      111 272 416
Unimodal      9
UNIT      427
Unit vector      56 142 143
Universal kriging      248 250 252 300—303 319 511 512
Unsupervised learning      410
Upper triangular matrix      251
Variability      41
Variable name      293
Variable selection      439
Variance      10 105 107 111 135 148 151 191 240 242 359 368
Variance-covariance matrix      272 416 445 452
Variate      130
Variogram      244
Vector space      443
Weierstrass polynomial approximation theorem      39
Weight      24 81 133 135 139 146 177 186 197 241 427 432 438 501
Weight decay      427
Weight diagram      143 227
Weight diagram vector      143
Weight function      49
Weighted average      32 55 104 238 240 477
Weighted least squares (WLS) method      372
Within-group covariance matrix      439
Within-group variance      440
Woofer      191 222
Working directory      307
Working response vector      372
Working value (working response, pseudo-response variable, or adjusted dependent variable)      372
Yellow ocher      186
Yield      326
Young’s modulus      167
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