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| Авторизация |
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| Поиск по указателям |
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| Eubank R.L. — Nonparametric regression and spline smoothing |
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| Предметный указатель |
Acceleration curve 222
Akaike information criterion 65
Asymptotic normality for kernel estimators 195 196
Asymptotic normality for series estimators 105
Asymptotic normality for smoothing splines 268 287
Bandwidth, asymptotically optimal 169 173 175 186 187
Bandwidth, convergence rates for estimators 181 183
Bandwidth, definition of 157
Bandwidth, estimation by cross validation 179
Bandwidth, for derivative estimation 188 219 220 222
Bandwidth, for smoothing splines 237 240 249 258
Bandwidth, plug-in estimators 184 185
Bandwidth, variable 185 194 258
Bias reduction lemma 131
Bias reduction lemma, for boundary bias removal 132 178 217 259 286
Bias reduction lemma, for estimation in partial linear models 137 203 223 278
Boundary bias for kernel estimators 170
Boundary bias for smoothing splines 254 259
Boundary bias for trigonometric regression estimators 102
Boundary bias removal by bias reduction lemma 132 178 217
Boundary bias removal by the generalized jack-knife 217
Boundary kernel 171 177 187 188 190 192 217—220
Central limit theorem 6 104
Complete orthonormal sequence 75
Confidence bands for kernel estimators, bias corrected 200
Confidence bands for kernel estimators, Bonferroni 200
Confidence bands for least squares splines 305
Confidence bands for series estimators 111
Confidence intervals for kernel estimators, bias corrected 197
Confidence intervals for kernel estimators, normal theory 196
Confidence intervals for least squares splines 299 305
Confidence intervals for parameters in a partial linear model 140 206
Confidence intervals for series estimators 82 96 106 128
Confidence intervals for series estimators, Bonferroni bias correction 108 128
Confidence intervals for smoothing splines Bayesian 265 268 287
Confidence intervals for smoothing splines Bayesian, normal theory 268 287
Cook’s distance 94 125 270
Cross validation 43
Deconvolution 274
Demmler — Reinsch representation of a smoothing spline 234 237
Derivative estimation using kernel estimators 188
Derivative estimation using smoothing splines 274
Epanechnikov kernel 176
Fourier coefficient, definition of 77 78
Fourier coefficient, estimation bias 106
Fourier coefficient, estimation of 80 87
Fourier coefficient, inference for 82 111 128
Fourier coefficient, rate of decay 101 129
Fourier series 77 79
Fourier series estimator, definition of 80
Fourier series estimator, relation to kenel estimators 162
Fourier series estimator, relation to smoothing splines 234
Generalized cross validation 43
Generlized linear models 277
Growth curve 192
GSJS variance estimator 49
Hutchinson/de Hoog algorithm 246
Interaction splines 277
Kernel, boundary 171
Kernel, for derivative estimation 188
| Kernel, for least squares splines 304
Kernel, for local linear regression 190
Kernel, for smoothing splines 237 247 258
Kernel, higher order 186
Kernel, minimum variance 176
Kernel, optimal 176
Kernel, second order 157
Laplacian smoothing splines 276
Legendre polynomials 76
loss 28
Mallow’s  39
Method of regularization 274
Nadaraya — Watson estimator 160 194 211
Natural boundary conditions 258 282
Order of a series estimator 83
Order of a series estimator, asymptotically optimal 100 129
Order of a series estimator, estimation of 84 85 128
Order of a spline 281
Order of an estimator 16
Order selection test 115
Partial spline 278
Pseudo-residuals 49
Regression curve 2
Regression function 2
Regression nonparametric 3
Regression ridge 34
Regression simple linear 3
Risk, definition of 14 28
Risk, estimation of 39
Risk, global convergence rate for kernel estimators 173 175 187
Risk, global convergence rate for local linear regression 190
Risk, global convergence rate for polynomial regression 129
Risk, global convergence rate for polynomial-trigonometric regression 134
Risk, global convergence rate for smoothing splines 253 258
Risk, global convergence rate for trigonometric regression 100
Risk, global convergence rate, optimal 16
Risk, integrated 30
Risk, pointwise convergence rate for kernel estimators 168 175 186
Risk, pointwise convergence rate for smoothing splines 252
Risk, prediction 29
Risk, prediction, estimation of 39 42 44
Schwarz criterion 55 56 58 61 91 114 149
Smoothing parameter, asymptotically optimal 253 254
Smoothing parameter, definition of 228
Smoothing parameter, estimation by cross validation 239
Smoothing parameter, estimation by generalized maximum likelihood 262 287
Smoothing parameter, relation to bandwidth 237 240
Speckman’s minimax estimator 259
Spline, B-spline 300
Spline, definition of 281
Spline, interaction 277
Spline, knots 281
Spline, natural 281
Spline, order of 281
Spline, partial 278
Spline, thin plate 276
Taylor’s Theorem 121
Thin plate splines 276
Twicing 219
Unbiased risk criterion 39
Variable selection 31 42 44 51
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