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Optimal subsampling design for polynomial regression in one covariate

Author

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  • Torsten Reuter

    (Otto von Guericke University Magdeburg)

  • Rainer Schwabe

    (Otto von Guericke University Magdeburg)

Abstract

Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important. In this paper we construct D-optimal subsampling designs for polynomial regression in one covariate for invariant distributions of the covariate. We study quadratic regression more closely for specific distributions. In particular we make statements on the shape of the resulting optimal subsampling designs and the effect of the subsample size on the design. To illustrate the advantage of the optimal subsampling designs we examine the efficiency of uniform random subsampling.

Suggested Citation

  • Torsten Reuter & Rainer Schwabe, 2023. "Optimal subsampling design for polynomial regression in one covariate," Statistical Papers, Springer, vol. 64(4), pages 1095-1117, August.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:4:d:10.1007_s00362-023-01425-0
    DOI: 10.1007/s00362-023-01425-0
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    References listed on IDEAS

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    1. Pronzato, Luc, 2004. "A minimax equivalence theorem for optimum bounded design measures," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 325-331, July.
    2. HaiYing Wang & Min Yang & John Stufken, 2019. "Information-Based Optimal Subdata Selection for Big Data Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 393-405, January.
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    Cited by:

    1. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Oliveira, Nuno M.C., 2024. "Using hierarchical information-theoretic criteria to optimize subsampling of extensive datasets," LSE Research Online Documents on Economics 121641, London School of Economics and Political Science, LSE Library.

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