Eubank R.L. — Nonparametric regression and spline smoothing :: Электронная библиотека попечительского совета мехмата МГУ

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Eubank R.L. — Nonparametric regression and spline smoothing

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Название: Nonparametric regression and spline smoothing

Автор: Eubank R.L.

Аннотация:

This textbook for a graduate level introductory course on data smoothing covers series estimators, kernel estimators, smoothing splines, and least-squares splines. The new edition deletes most of the asymptotic theory for smoothing splines and smoothing spline variants, and adds order selection for hierarchical models, estimation in partially linear models, polynomial-trigonometric regression, new results on bandwidth selection, and locally linear regression. The first edition was published as (1988).

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1999

Количество страниц: 337

Добавлена в каталог: 29.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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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