Optimal designs for estimating the coefficients of the lower frequencies in trigonometric regression models

被引：10

作者：

Dette, Holger ^{[1
]}

Melas, Viatcheslav B.

Shpilev, Piter

机构：

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

[2] St Petersburg State Univ, Dept Math, St Petersburg, Russia

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2007年 / 59卷 / 04期

关键词：

trigonometric regression model; c-Optimal design; chebyshev approximation; two dimensional shape analysis;

D O I：

10.1007/s10463-006-0068-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the performance of the D-optimal design with respect to the estimation of the lower order coefficients is investigated. The results give a complete answer to an open question which was recently raised in the literature.

引用

页码：655 / 673

页数：19

共 16 条

[1] Optimal designs for estimating the coefficients of the lower frequencies in trigonometric regression models
Holger Dette
Viatcheslav B. Melas
Piter Shpilev
Annals of the Institute of Statistical Mathematics, 2007, 59 : 655 - 673
[2] Optimal designs for estimating individual coefficients in polynomial regression with no intercept
Dette, Holger
Melas, Viatcheslav B.
Shpilev, Petr
STATISTICS & PROBABILITY LETTERS, 2020, 158
[3] Optimal designs for estimating individual coefficients in polynomial regression - a functional approach
Dette, H
Melas, VB
Pepelyshev, A
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2004, 118 (1-2) : 201 - 219
[4] Optimal designs for a class of nonlinear regression models
Dette, H
Melas, VB
Pepelyshev, A
ANNALS OF STATISTICS, 2004, 32 (05): : 2142 - 2167
[5] A geometric characterization of optimal designs for regression models with correlated observations
Holland-Letz, Tim
Dette, Holger
Pepelyshev, Andrey
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2011, 73 : 239 - 252
[6] Local c- and E-optimal designs for exponential regression models
Dette, Holger
Melas, Viatcheslav B.
Pepelyshev, Andrey
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2006, 58 (02) : 407 - 426
[7] Totally positive regression: E-optimal designs
Heiligers B.
Metrika, 2002, 54 (3) : 191 - 213
[8] Totally positive regression:: E-optimal designs
Heiligers, B
METRIKA, 2001, 54 (03) : 191 - 213
[9] Computing E-optimal polynomial regression designs
Heiligers, B
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1996, 55 (02) : 219 - 233
[10] E-OPTIMAL DESIGNS IN WEIGHTED POLYNOMIAL REGRESSION
HEILIGERS, B
ANNALS OF STATISTICS, 1994, 22 (02): : 917 - 929

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