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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
10-fold cross-validation      418 432 460 471 472 526
Accumulated temperature      328
ACE (Alternating Conditional Expectation) algorithm      280
ACE algorithm      323
Additive model      2 258 261 264 270 283 304 423 514
Adjusted independent variable regression      372
AICc      378
AICc (Corrected AIC)      128 376
Akaike’s Information Criterion (AIC)      121 125
Akima’s method      234 237 252 291 507
Aliasing error      15 186
Anchor      8 360 369
Anisotropy      245
Argument      81 204 294 345 387
Array      403
artificial intelligence      20
Automated Meteorological Data Aquisition System (AMeDAS)      8 13 25 96
Average mean squared error      114
Average Predictive Squared Error (APSE)      115
B-spline      179 207 218 266 277 281 305 320 484 486 502 526
B-spline (B-splines)      88 163 264 343 394 502
B-spline basis      473
Backfitting      264
Bagging      435 463 471 526
Band matrix      483
Bandwidth      49 131 133 191 234 288 367 376 377
Base temperature      328
Bases      180
Basis      58 179 180 218 437 474 484 526
Bayesian inference      414
Bayes’ decision rule      414 434
Bayes’ Theorem      414
Bending elastic energy      158
Bending moment diagram      167
Bernoulli distribution      421 425
Between-group covariance matrix      439
Between-group variance      440
Bias      105 107 112 135 150 151 191 238 240
bin      327 360 520
Binomial distribution      9 390 421 427 471
Binomial factor      27 421
Binomial filter      27 82 95 98 110 226 363 501
Binwidth      8 327 360
Bisquare weight function      197
Bisquare weight function (biweight, bisquare)      140
Block Gauss — Seidel method      264
Bootstrap data      435
Bootstrap sample      435 464 471
Boundary (bin edge)      9
Boundary bias      146 379
Boundary knot (boundary breakpoint)      207 305
Calculus of variations      172
Canonical coefficient      272
Canonical correlation analysis      271 276 277 309 440 515
Canonical correlation coefficient      272
Canonical variate      272 439 440 466 526
Canonical weight      272
Cardinal spline      480
Cardinal-spline basis      480 482
Centered smoother      261 323
Central limit theorem      12 407
Characteristic equation      56
Cholesky decomposition      179 251
class      410
Classification      410
Coefficient      245
Coefficient of correlation      42 243 271
Coefficient of determination      42
Complementary log-log transformation      471
Complexity parameter      432 460 526
Component      212 289 349 394
Concentrated load      166
Conditional density      130
Conditional probability density function      130
Correlation      238 239
Correlogram      243
Cosine kernel      396
Cosine wave      5
Cost-complexity measure      432
Covariance      119 244 248
Covariance matrix      272
Covariogram      243
Cross-entropy      430
Cross-validated deviance      368
Cross-validation      123 125 189 191
Cross-Validation (CV)      115 319
Csv (comma separated value format)      95
Cubic equation      38
Cubic smoothing spline (cubic smoothing splines)      170 234 319
Cubic spline function      46 152 227
Curvature      158 167
CV      120 135 234
Daily average temperature      13
DATA      103
Data analysis      10
Data frame      85 88—90 203 204 209 224 288—291 293 296 307 308 316 390 392 394
Data set      105
Database      307
Daytime      335
De Boor — Cox algorithm      474
Decision boundary      412
Defined region      159 475
Deflection curve      166
Degrees of freedom      118 218 307 322 376 520
Delta function      114 381
Density function      2
Dependent variable      2
Design matrix      33 86 100 140 319 320 330 347 349 353 375 487
Development      20
Developmental stage      335
Deviance      367 368 376 430 520
Diagonal element      42 117
Diagonal matrix      56 141 330
Diagonalization      56
Discrete      15
Discriminant coordinate      440
Discriminant function      414 422
Discrimination      410
Dispersion parameter, scale parameter      368
Effective accumulated temperature      328
Eigenequation      56
Eigenvalue      98 229 272
Eigenvalue (characteristic value)      56 144 258 441 502
Eigenvalue problem      272 277 279
Eigenvector      56 98 258 272 441
Elastic energy      158 167
Element      2 32 134 239 325 359
Empirical correlogram      252
Empirical correlogram (sample correlogram)      244
Empirical variogram      252
Empirical variogram (sample variogram)      244
Equivalent degrees of freedom      269 307
Equivalent kernel      117 133 143 227 480
Equivalent number of freedom      119
Error      2 104
Estimate (estimated value)      15 23 103 231 327 359 473 502
Estimation      2
Euclidean distance      297 434
Exchange rate      4
Expectation      105 115 125 131 362 378 421
Expectation function      363
Expected mean log-likelihood      124 126
Explained variable      2
Explanatory variable      2
Exponential correlogram      245
Expression frame      392 394 402
Expression frame (top-level frame, frame I)      88 307 390
Extrapolation      181 475
Factorial      27 151 185 362
Feature selection (feature extraction)      410
Feature vector (feature pattern)      410
Figure of merit      286
First canonical correlation coefficient      272
First canonical variate      272
First degree spline function      43
First derivative function      152
Fisher scoring procedure (Fisher scoring algorithm)      373 422
Fitting      20 32 112 331 360
Flexural rigidity      167
Flexural rigidity of plate      235
Flowering day      326
Form of equation      18
Fourier series      6 16
Fourier transform      5 67
frequency      8 325 327 339 360 362 363 367 378 379 387 390 392 394 395 520
Function      307
Functional data analysis      326
Functional form      13
Functional space      476
Fuzzy inference      334
Fuzzy logic      20
Gamma distribution      390
Gamma function      172
Gamma function (Euler’s gamma function)      84
Gauss — Seidel method      258 263 264 269 304 306 514
Gaussian correlogram      245
Gaussian function      49 132 134 135 140 179 233 343 365 378 418 453
Gaussian kernel      146
GCV      120 135 234 327 376
GCVPACK      185 211 236 270 294 321 330 344 503 517
Generalized additive model      377 394 423 520
Generalized cross-validated deviance      376
Generalized Cross-Validation (GCV)      118 376
Generalized least squares      240 252
Generalized linear regression      371 373 389—391 421 422 430 517 518
Generalized local log-likelihood      367
Generalized nonparametric regression      378 393 519
Generalized variance      416
Geometrical moment of inertia      167
Geostatistics      238
Gibbs effect      67
Gini diversity index      431
Golden ratio search      184 216 236 294 331 350
Gradient      383 403
Green function (Green’s function)      172 473 484
Growth      20
Hat matrix      32 39 40 53 116 118 124 125 134 135 143 146 176 177 180-182 184 189 200 204 205 215 220 234 242 248 258 260 261 263 264 269 270 273 280 305 330 375 437 483 502
Heading day      326 335 336
Hessian matrix      384 403
Hidden layer      427
histogram      8 360 363 379 385 517
Hooke’s law      167 174
Hyperplane      78
Idempotent      40 57 58 78 98 260 264 266 269
Identity matrix      43 53 56 175 229 241 260 321
Identity transformation (identical transformation)      375
improvement      430 432
Impurity      430 431
Independent variable      2
Influence      117
Inner product      42 259 271 337
Input argument      212 300 345
Input output argument      212 345
Interestingness      286
Internal knot      89
Internal knot (internal breakpoint)      45 207 305
Interpolation      15 156 474
Interpolation method      238
Inverse gaussian distribution      390
Inverse matrix      53 417 418 471
Invertible matrix      56 240
Iogit transformation      421 471
Isotropy      245
Iterative calculation      372
Iterative Reweighted Least Squares (IRLS) method      373 422
Joint density      130
Joint probability density function      130 229
Jugler cycle      5
K-nearest-neighbor classifier      435 472
K-nearest-neighbor distance      186 237
K-nearest-neighbor estimate      186
Kernel      151
Kernel density estimator      131 139
Kernel estimator      104 378
Kernel function      49 133—135 139 146 186 189 198 200 203 233 234 237 238 288 365 366 378 381 384 396 418
Kitchen cycle      5
Knot      181
Knot (break point)      245
Knot (breakpoint)      45 151 474 520
Kondratieff cycle      5
Kriging interpolation      238
Kullback — Leibler distance      367 376 430
Kullback — Leibler information      367 430
Kuznets cycie      5
Lagrange multiplier      242 441
Law of action and reaction      178
Learning      410
Least squares      112 117 118 123 125 229 245 260 263 273 275—277 370 438
Least squares (least square method)      16 32 111 239 327 359 437 478 482
Leave-one-out cross-validation      116
Leave-one-out method      116
Leverage (leverage value)      117 218
Likelihood      122 360 362 416
Likelihood cross-validation      124 381 407
Likelihood ratio      367
linear combination      60 78 117 179 371 421 474
Linear discriminant rule      417 447-449 471 524
Linear equation      38
Linear estimator      32 35 39 45 117 118 125 184 242 270 277 376
Linear model      18 421
Linear regression      18
Linear splines function      43
Linearly independent      441 443 474 480
Link function      371 373 375 390 422 459 471
LINPACK      212 330 349
Local adaptation      195
Local constant estimation      139
Local cross-validated residual      192
Local cross-validation      192 223
Local fitting      49
Local frame      307
Local likelihood      424
Local linear regression      47 49 89 98 202 205 226 234 287 289 502 507
Local log-likelihood      367
Local polynomial regression      104 139 181 227 232
Local regression      47
Local support      474
Local-scoring procedure      424
LOESS      104 177 186 191 195 219 223 224 237 269 295 378 394 505 506 509
Log-likelihood      122 362 364 366 367
Log-linear model      372
Logical object      84
Logistic discrimination      424
Logistic function      336
Logistic model      421
Logistic regression      421 458 525
Logit model      421
Look-up degree of freedom      119
Lower triangular matrix      251
LOWESS (LOcally WEighted Scatterplot Smoother)      104 195 223 224 237 506
LOWESS (robust version of LOESS)      237
Mask      307
Maximum likelihood estimate      122
Maximum likelihood estimator      272
Maximum likelihood procedure (maximum likelihood method)      10 122 360 363 425
Maximum log-likelihood      122
Mean Integrated Squared Error      114
Mean squared error      110
Mean squared error (MSE)      106
Median      197
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