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Robustness of a truncated estimator for the smaller of two ordered means

Author

Listed:
  • Yasuyuki Hamura

    (Kyoto University)

  • Tatsuya Kubokawa

    (University of Tokyo)

Abstract

In this note, we consider the problem of estimating the smaller of two ordered means. Such problems frequently arise in applications where, for example, aggregated data are observed. In order to combine information from direct and indirect observations, we use the Stein-type truncated estimator. We show that it dominates the direct estimator for distributions with log-concave or log-convex densities.

Suggested Citation

  • Yasuyuki Hamura & Tatsuya Kubokawa, 2023. "Robustness of a truncated estimator for the smaller of two ordered means," Statistical Papers, Springer, vol. 64(6), pages 2225-2244, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01371-3
    DOI: 10.1007/s00362-022-01371-3
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    References listed on IDEAS

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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    3. Shonkwiler, J.S., 2016. "Variance of the truncated negative binomial distribution," Journal of Econometrics, Elsevier, vol. 195(2), pages 209-210.
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