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Improving upon the effective sample size based on Godambe information for block likelihood inference

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  • Rahul Mukerjee

    (Indian Institute of Management Calcutta)

Abstract

We consider the effective sample size, based on Godambe information, for block likelihood inference which is an attractive and computationally feasible alternative to full likelihood inference for large correlated datasets. With reference to a Gaussian random field having a constant mean, we explore how the choice of blocks impacts this effective sample size. This is done by introducing a column-wise blocking method which spreads out the spatial points within each block, instead of keeping them close together as the existing row-wise blocking method does. It is seen that column-wise blocking can lead to considerable gains in effective sample size and efficiency compared to row-wise blocking, while retaining computational simplicity. Analytical results in this direction are obtained under the AR (1) model. The insights so found facilitate the study of other one-dimensional correlation models as well as correlation models on a plane, where closed form expressions are intractable. Simulations are seen to provide support to our conclusions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-023-01328-6
    DOI: 10.1007/s00180-023-01328-6
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    References listed on IDEAS

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    1. 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).
    2. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
    3. Caragea, Petruta C. & Smith, Richard L., 2007. "Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1417-1440, August.
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    1. 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).

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