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Estimating the covariance of bivariate order statistics with applications

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  • Hutson, Alan D.

Abstract

In this note we develop a new analytic bootstrap-type method for estimating the covariance between the bivariate order statistics Xr:n and Ys:n. Correlation and regression estimators follow straightforward from this result. An easy-to-use method for calculating the nonparametric percentile confidence regions for bivariate quantiles is developed and illustrated using biological data. A specific case of interest is the application to bivariate medians, i.e., correlated marginal medians.

Suggested Citation

  • Hutson, Alan D., 2000. "Estimating the covariance of bivariate order statistics with applications," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 195-203, June.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:2:p:195-203
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    References listed on IDEAS

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    1. A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    2. Maritz, J. S., 1991. "Estimating the covariance matrix of bivariate medians," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 305-309, October.
    3. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.
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