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Biometrika 2005 92(1):149-158; doi:10.1093/biomet/92.1.149
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© 2005 Biometrika Trust

Standard errors and covariance matrices for smoothed rank estimators

B. M. Brown and You-Gan Wang

Department of Statistics and Applied Probability, National University of Singapore, Singapore 117543 stabbm{at}nus.edu.sg, stawyg{at}nus.edu.sg

A ‘pseudo-Bayesian’ interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

Key Words: Covariance estimator; Estimating function; Induced smoothing; Kernel estimator; Linearisation; One step estimation; Rank estimation; Sandwich formula; Second-order convergence; Standard error; Wilcoxon estimator

Received August 2003. Revised May 2004.


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