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Estimating the variance of the sample median, discrete case

Author

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  • Huang, J. S.

Abstract

Variance of the sample median from discrete distributions is estimated by the bootstrap and by the jackknife methods. For asymmetric Bernoulli distributions, it is shown that both estimators grossly overestimate the true variance, with the bootstrap estimator getting progressively worse than the jackknife as the sample size gets larger. For the symmetric Bernoulli, the jackknife continues to overestimate the variance, while the bootstrap underestimates, tending to two thirds the true variance in the limit. Numerical evidence suggests that the same limiting behavior is shared by a large class of discrete distributions including the binomial, Poisson and geometric.

Suggested Citation

  • Huang, J. S., 1991. "Estimating the variance of the sample median, discrete case," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 291-298, April.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:4:p:291-298
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    Cited by:

    1. Gabriel Montes Rojas & Andrés Sebastián Mena, 2020. "Density estimation using bootstrap quantile variance and quantile-mean covariance," Documentos de trabajo del Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET) 2020-50, Universidad de Buenos Aires, Facultad de Ciencias Económicas, Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET).

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