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Biometrika 1994 81(2):341-350; doi:10.1093/biomet/81.2.341
© 1994 by Biometrika Trust
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A resampling method based on pivotal estimating functions

M. I. PARZEN, L. J. WEI and Z. YING

Graduate School of Business, University of Chicago Chicago, Illinois 60637, U. S.A.
Department of Biostatistics, Harvard University Boston, Massachusetts 02115, U. S.A.
Department of Statistics, University of Illinois Champaign, Illinois 61820, U. S.A.

Suppose that, under a semiparametric model setting, one is interested in drawing inferences about a finite-dimensional parameter vector ß based on an estimating function. Generally a consistent point estimator ß{circumflex} for ßo, the true value for ß, can be easily obtained by finding a root of the corresponding estimating equation. To estimate the variance of ß{circumflex}, however, may involve complicated and subjective nonparametric functional estimates. In this paper, a general and simple resampling method for inferences about ßO based on pivotal estimating functions is proposed. The new procedure is illustrated with the quantile and rank regression models. For both cases, our proposal can be easily and efficiently implemented with existing statistical software.

Key Words: Bootstrap • Pivot • Quantile regression • Rank regression


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