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Biometrika 2004 91(4):943-954; doi:10.1093/biomet/91.4.943
© 2004 by Biometrika Trust
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Statistical inference based on non-smooth estimating functions

L. Tian1, J. Liu2, Y. Zhao3 and L. J. Wei3

1 Department of Preventive Medicine, Northwestern University, 680 N. Lake Shore Drive, Suite 1102, Chicago, Illinois 60611, U.S.A. lutian{at}northwestern.edu, 2 Department of Statistics, Harvard University, Science Center 6th floor, 1 Oxford Street, Cambridge, Massachusetts 02138, U.S.A. jliu{at}stat.harvard.edu, 3 Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. mzhao{at}hsph.harvard.edu, wei{at}sdac.harvard.edu

When the estimating function for a vector of parameters is not smooth, it is often rather difficult, if not impossible, to obtain a consistent estimator by solving the corresponding estimating equation using standard numerical techniques. In this paper, we propose a simple inference procedure via the importance sampling technique, which provides a consistent root of the estimating equation and also an approximation to its distribution without solving any equations or involving nonparametric function estimates. The new proposal is illustrated and evaluated via two extensive examples with real and simulated datasets.

Key Words: Importance sampling; L1-norm; Linear regression for censored data; Resampling

Received September 2003. Revised April 2004.


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