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Consistency of the k-Nearest Neighbor Classifier for Spatially Dependent Data

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Abstract

The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data. Some spatial mixing conditions are considered, and under such spatial structures, the well known k-nearest neighbor rule is suggested to classify spatial data. We established consistency and strong consistency of the classifier under mild assumptions. Our main results extend the consistency result in the i.i.d. case to the spatial case.

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Acknowledgements

The authors would like to thank the anonymous referees whose valuable comments led to an improved version of the paper.

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Authors and Affiliations

  1. INRAE, Institut Agro, MISTEA, Université Montpellier, Montpellier, France

    Ahmad Younso

  2. Department of Mathematical Statistics, Faculty of Sciences, Damascus University, Damascus, Syria

    Ahmad Younso

  3. Department of Mathematics, Faculty of Sciences, Tishreen University, Lattakia, Syria

    Ziad Kanaya & Nour Azhari

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  1. Ahmad Younso
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  2. Ziad Kanaya
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  3. Nour Azhari
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Correspondence to Ahmad Younso.

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Younso, A., Kanaya, Z. & Azhari, N. Consistency of the k-Nearest Neighbor Classifier for Spatially Dependent Data. Commun. Math. Stat. 11, 503–518 (2023). https://doi.org/10.1007/s40304-021-00261-8

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  • DOI: https://doi.org/10.1007/s40304-021-00261-8

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