D-optimal designs for full and reduced Fourier regression models
type: Item
instance of: scholarly article
title: D-optimal designs for full and reduced Fourier regression models
zbMATH Open document ID: 1383.62185
author: Xiaoli Shang
author: Xiaojian Xu
published in: Statistical Papers
publication date: 2017-12-13T00:00:00Z
review text: Consider trigonometric regression models having basis functions of the type \(1\), \(\sin(jt)\), \(\cos(jt)\), \(j=1,\dots,m\), unknown parameters \(\beta_0,\beta_{2j-1}\), \(\beta_{2j}\), \(j=1,\dots,m\), resp., sets of design support points \(I=\{t_1,\dots,t_n\}\), and uncorrelated, zero-mean random errors \(\epsilon_t\), \(t \in I\), with variance \(\sigma^2\). Considering designs, represented by discrete probability measures \(\xi\) on \(I\), D-optimal designs -- minimizing the determinant of the covariance matrix of the parameter estimator -- are given for different types of trigonometric regression models. Especially, D-optimal designs for estimating pairs of coefficients related to sine and cosine terms are taken into account. Comparisons of the models under considerations are presented.
reviewed by: Kurt Marti
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62K05
zbMATH DE Number: 6818155
zbMATH Keywords: linear regression
zbMATH Keywords: trigonometric regression
zbMATH Keywords: D-optimal design
MaRDI profile type: Publication
full work available at URL: s00362-015-0727-6
OpenAlex ID: W2274139806
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DOI: 10.1007/S00362-015-0727-6
description: scientific article; zbMATH DE number 6818155