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Biometrika 2001 88(2):381-390; doi:10.1093/biomet/88.2.381
© 2001 by Biometrika Trust
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A simple resampling method by perturbing the minimand

Zhezhen Jin1, Zhiliang Ying2 and L.J. Wei3

1 Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.Azjin{at}hsph.harvard.edu 2 Department of Statistics, Columbia University, 2990 Broadway, New York, New York 10027, U.S.A.zying{at}stat.columbia.edu 3 Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. wei{at}hsph.harvard.edu

Suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a U-process structure.The covariance matrix of the estimator is generally a function of the underlying density function, which may be difficult to estimate well by conventional methods. In this paper, we present a simple resampling method by perturbing the objective function repeatedly. Inferences of the parameters can then be made based on a large collection of the resulting optimisers. We illustrate our proposal by three examples with a heteroscedastic regression model.

Key Words: Bootstrap; Heteroscedastic regression; Lp norm; Resampling method; Truncated regression; U-process

Received February 2000. Revised August 2000


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