A fast procedure for calculating importance weights in bootstrap sampling

Authors:
Hua Zhou;Kenneth Lange
Affiliations:
Department of Human Genetics, University of California, Los Angeles, CA 90095-1766, United States;Departments of Biomathematics, Human Genetics, and Statistics, University of California, Los Angeles, CA 90095-1766, United States
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

Importance sampling is an efficient strategy for reducing the variance of certain bootstrap estimates. It has found wide applications in bootstrap quantile estimation, proportional hazards regression, bootstrap confidence interval estimation, and other problems. Although estimation of the optimal sampling weights is a special case of convex programming, generic optimization methods are frustratingly slow on problems with large numbers of observations. For instance, interior point and adaptive barrier methods must cope with forming, storing, and inverting the Hessian of the objective function. In this paper, we present an efficient procedure for calculating the optimal importance weights and compare its performance to standard optimization methods on a representative data set. The procedure combines several potent ideas for large-scale optimization.