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
收藏
页码：655 / 673
页数：19
相关论文
共 22 条
[1]  
[Anonymous], 1959, AM MATH SOC C PUBLIC
[2]   Quantitative evaluation of apple (Malus × domestica Borkh.) fruit shape by principal component analysis of Fourier descriptors [J].
Currie A.J. ;
Ganeshanandam S. ;
Noiton D.A. ;
Garrick D. ;
Shelbourne C.J.A. ;
Oraguzie N. .
Euphytica, 2000, 111 (3) :221-227
[3]   Optimal designs for estimating individual coefficients in polynomial regression - a functional approach [J].
Dette, H ;
Melas, VB ;
Pepelyshev, A .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2004, 118 (1-2) :201-219
[4]  
Dette H, 2003, ANN STAT, V31, P1669
[5]   D-optimal designs for trigonometric regression models on a partial circle [J].
Dette, H ;
Melas, VB ;
Pepelyshev, A .
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2002, 54 (04) :945-959
[6]  
Eubank RL., 1999, NONPARAMETRIC REGRES
[7]   EQUIVALENCE OF D-OPTIMAL DESIGN MEASURES FOR 3 RIVAL LINEAR-MODELS [J].
HILL, PDH .
BIOMETRIKA, 1978, 65 (03) :666-667
[8]  
JOLLEY LBW, 1961, SUMMATION SERIES
[9]  
Karlin S., 1966, TCHEBYCHEFF SYSTEMS
[10]   GENERAL EQUIVALENCE THEORY FOR OPTIMUM DESIGNS (APPROXIMATE THEORY) [J].
KIEFER, J .
ANNALS OF STATISTICS, 1974, 2 (05) :849-879
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