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<p>Interval-valued data, characterized by intrinsic measurement imprecision, uncertainty, and variability, are common in real-world applications. This study introduces a novel spatial autoregressive model tailored for interval-valued data, unifying and generalizing several existing frameworks. To address the limitations of interval representations, we develop a joint quasi-maximum likelihood estimation method that holistically incorporates complete interval information through both center and radius parameters. Crucially, we introduce a novel <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11222_2025_10688_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-type distance metric to quantify interval variance, which systematically captures richer intra-interval information compared to classical Euclidean interval distance metric. The asymptotic properties of the estimators under regularity conditions are established, ensuring statistical robustness. Numerical experiments on synthetic datasets demonstrate the superiority of the proposed method over conventional approaches in prediction accuracy and information retention. Empirical validation on real spatial interval datasets-urban house price domain-confirms the efficiency of the parameter estimation framework and the operational viability of the proposed model.</p>

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Spatial autoregressive model for interval-valued data and applications

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Jinjin Zhang,
  • Kun Li,
  • Aibing Ji

摘要

Interval-valued data, characterized by intrinsic measurement imprecision, uncertainty, and variability, are common in real-world applications. This study introduces a novel spatial autoregressive model tailored for interval-valued data, unifying and generalizing several existing frameworks. To address the limitations of interval representations, we develop a joint quasi-maximum likelihood estimation method that holistically incorporates complete interval information through both center and radius parameters. Crucially, we introduce a novel \(L_2\) L 2 -type distance metric to quantify interval variance, which systematically captures richer intra-interval information compared to classical Euclidean interval distance metric. The asymptotic properties of the estimators under regularity conditions are established, ensuring statistical robustness. Numerical experiments on synthetic datasets demonstrate the superiority of the proposed method over conventional approaches in prediction accuracy and information retention. Empirical validation on real spatial interval datasets-urban house price domain-confirms the efficiency of the parameter estimation framework and the operational viability of the proposed model.