Selection of variables in a multivariate inverse regression problem
type: Item
instance of: scholarly article
title: Selection of variables in a multivariate inverse regression problem
zbMATH Open document ID: 0613.62098
author: Yasunori Fujikoshi
author: Ryuei Nishii
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: We assume that a set of p response variables \({\mathfrak y}=(y_ 1,...,y_ p)\) is linearly determined by a set of q explanatory variables \({\mathfrak x}=(x_ 1,...,x_ q)\), and that a calibration sample of N observations of \({\mathfrak x}\) and \({\mathfrak y}\) is available. A new observation \({\mathfrak y}\) is available at a single unknown \({\mathfrak x}\), and it is desired to estimate \({\mathfrak x}.\) Under this set-up we propose two methods for selection of the ''best'' subset of \({\mathfrak y}\). One is based on the asymptotic mean squared error of the classical estimate. The other uses Akaike's information criterion for selection of models. The two methods are applied to the wheat quality data analysed by \textit{P. J. Brown} [J. R. Stat. Soc., Ser. B 44, 287-321 (1982; Zbl 0511.62083)].
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 3992707
zbMATH Keywords: multivariate inverse regression
zbMATH Keywords: variable selection
zbMATH Keywords: asymptotic mean squared error
zbMATH Keywords: Akaike's information criterion
zbMATH Keywords: selection of models
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3992707