A comparison of some linear and nonlinear discrimination methods
type: Item
instance of: scholarly article
title: A comparison of some linear and nonlinear discrimination methods
zbMATH Open document ID: 0941.62112
author: Mantred Berres
published in: Computational Statistics
publication date: 2000-03-02T00:00:00Z
review text: Let \(Y\) be a response variable and \(X_1,\dots,X_k\) be predictor variables. The alternating conditional expectations (ACE) algorithm finds nonparametric functions \(\theta(Y)\) and \(\varphi_j (X)\) which minimize the expression \( E[\theta(Y)-\sum_{j=1}^k\varphi_j(X_j)]^2/E[\theta(Y)]^2. \) ACE may be considered as a nonlinear generalization of linear regression [\textit{L. Breiman} and \textit{J.H. Friedman}, J. Am. Stat. Assoc. 80, 580-619 (1985; Zbl 0594.62044)]. An analogous generalization for canonical correlations (OVERALS algorithm) is that one made by \textit{E. van der Burg, J. de Leeuw} and \textit{R. Verdegaal} [Psychometrika 53, No. 2, 177-197 (1988; Zbl 0718.62143)]. In this article these two nonlinear algorithms are compared with classical linear regression and canonical correlation methods to analyse the results of arthropod selectivity to pest trials. The transformations of variables determined by OVERALS were quite similar to the important transformations of ACE and were presumed to be reasonable.
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 1409656
zbMATH Keywords: nonlinear transformations
zbMATH Keywords: canonical correlations
zbMATH Keywords: multivariate regression
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1409656