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Abstract <p>This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5068_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Z}^{d}\)</EquationSource> <!--MMStat2570001Penda-m1--> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5068_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(d\geqslant 1\)</EquationSource> <!--MMStat2570001Penda-m2--> </InlineEquation>. We use a criterion that allows to characterize the subset of relevant variables as depending on two parameters, and we propose estimators for these parameters based on spatially dependent observations. We prove the consistency, under specified assumptions, of the method thus proposed. A simulation study made in order to assess the finite-sample behaviour of the proposed method with comparison to existing ones is presented.</p>

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Variable Selection in Multivariate Linear Regression Model for Spatially Dependent Data

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Jean Roland Ebende Penda,
  • Stéphane Bouka,
  • Guy Martial Nkiet

摘要

Abstract

This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in \(\mathbb{Z}^{d}\) with \(d\geqslant 1\) . We use a criterion that allows to characterize the subset of relevant variables as depending on two parameters, and we propose estimators for these parameters based on spatially dependent observations. We prove the consistency, under specified assumptions, of the method thus proposed. A simulation study made in order to assess the finite-sample behaviour of the proposed method with comparison to existing ones is presented.