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Is the effective sample size always less than n? A spatial regression approach

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  • Ferrer, Clemente
  • Vallejos, Ronny

Abstract

In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds n, which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size n does not exceed n. This property is desirable because it ensures the effectiveness of reduction measures.

Suggested Citation

  • Ferrer, Clemente & Vallejos, Ronny, 2025. "Is the effective sample size always less than n? A spatial regression approach," Statistics & Probability Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:stapro:v:218:y:2025:i:c:s0167715224002785
    DOI: 10.1016/j.spl.2024.110309
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    References listed on IDEAS

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    1. Letícia Ellen Dal Canton & Luciana Pagliosa Carvalho Guedes & Miguel Angel Uribe-Opazo & Tamara Cantu Maltauro, 2023. "Effective Sample Size with the Bivariate Gaussian Common Component Model," Stats, MDPI, vol. 6(4), pages 1-18, October.
    2. Egidi, Leonardo, 2022. "Effective sample size for a mixture prior," Statistics & Probability Letters, Elsevier, vol. 183(C).
    3. Acosta, Jonathan & Alegría, Alfredo & Osorio, Felipe & Vallejos, Ronny, 2021. "Assessing the effective sample size for large spatial datasets: A block likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    4. James Berger & M. J. Bayarri & L. R. Pericchi, 2014. "The Effective Sample Size," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 197-217, June.
    5. Faes, Christel & Molenberghs, Geert & Aerts, Marc & Verbeke, Geert & Kenward, Michael G., 2009. "The Effective Sample Size and an Alternative Small-Sample Degrees-of-Freedom Method," The American Statistician, American Statistical Association, vol. 63(4), pages 389-399.
    6. Rahul Mukerjee, 2024. "Improving upon the effective sample size based on Godambe information for block likelihood inference," Computational Statistics, Springer, vol. 39(2), pages 891-904, April.
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