The forward search and data visualization
type: Item
instance of: scholarly article
title: The forward search and data visualization
zbMATH Open document ID: 1053.62007
DOI: 10.1007/BF02915275
author: Anthony C. Atkinson
author: Marco Riani
published in: Computational Statistics
publication date: 2004-11-24T00:00:00Z
review text: The forward search procedure is based on the Mahalonobis norm of \(n\) data vectors \(y_i\), \[ d_i^2(m)=(y_i-\widehat\mu(m))^\top \widehat\Sigma^{-1}(m)(y_i-\widehat\mu(m)), \] where the means \(\widehat\mu(m)\) and covariances \(\widehat\Sigma(m)\) are estimated by a subset \(S(m)\) of \(m\) observations. At the \(m\)-th step of the procedure \(m+1\) observations with the smallest \(d_i^2(m)\) are taken as new \(S(m+1)\). The trajectories of \(d_i^2(m)\), \(m=m_0\), \(m_0+1,\dots,n\), are depicted at one display for all \(i=1,\dots m\). The authors discuss the use of such ``forward plots'' for the investigation of cluster structure and outlier detection. Applications to different real life and simulated examples are presented.
Mathematics Subject Classification ID: 62A09
Mathematics Subject Classification ID: 62-07
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 2118525
zbMATH Keywords: outlier detection
zbMATH Keywords: cluster structure
zbMATH Keywords: Mahalonobis distance
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2118525