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BLUE against OLSE in the location model: energy minimization and asymptotic considerations

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Abstract

The main purpose of the paper is to uncover the connections between kriging, energy minimization and properties of the ordinary least squares and best linear unbiased estimators in the location model with correlated observations. We emphasize the special role of the constant function and illustrate our results by several examples.

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Acknowledgements

The work of the first author was partly supported by project INDEX (INcremental Design of EXperiments) ANR-18-CE91-0007 of the French National Research Agency (ANR). The authors are grateful to Toni Karvonen (University of Helsinki) for useful advice and especially for proposing a family of translation- invariant kernels with non-convex functions \(\Psi \) and \(\textrm{1}_{{\mathscr {X}}}\in {{{\mathcal {P}}}}_K\) used in Example 1.

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Authors and Affiliations

  1. Université Côte d’Azur-CNRS, Laboratoire I3S, Sophia Antipolis, France

    Luc Pronzato

  2. School of Mathematics, Cardiff University, Cardiff, UK

    Anatoly Zhigljavsky

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  1. Luc Pronzato
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  2. Anatoly Zhigljavsky
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Correspondence to Luc Pronzato.

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Pronzato, L., Zhigljavsky, A. BLUE against OLSE in the location model: energy minimization and asymptotic considerations. Stat Papers 64, 1187–1208 (2023). https://doi.org/10.1007/s00362-023-01423-2

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