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A Fast Procedure for Calculating Importance Weights in Bootstrap Sampling.

Hua Zhou¹, Kenneth Lange

¹Department of Human Genetics University of California Los Angeles, CA 90095-1766 huazhou@ucla.edu.

Computational Statistics & Data Analysis

|November 16, 2010

Summary

This summary is machine-generated.

Importance sampling improves bootstrap estimates by optimizing sampling weights. This study introduces an efficient method for calculating these weights, outperforming standard optimization techniques for large datasets.

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Area of Science:

Statistical Methods
Computational Statistics

Background:

Importance sampling is crucial for reducing variance in bootstrap estimates.
Applications include quantile estimation, regression, and confidence interval calculation.
Optimal sampling weight estimation is a convex programming problem, but generic methods are slow for large datasets.

Purpose of the Study:

To present an efficient procedure for calculating optimal importance weights.
To compare the performance of this new procedure against standard optimization methods.

Main Methods:

Developed an efficient procedure combining large-scale optimization techniques.
Evaluated performance on a representative dataset using standard optimization methods for comparison.

Main Results:

The proposed procedure offers significant efficiency gains in calculating optimal importance weights.
Demonstrated superior performance compared to generic interior point and adaptive barrier methods on large datasets.

Conclusions:

The novel procedure provides a computationally efficient solution for optimal importance weight calculation.
This advancement is particularly beneficial for large-scale statistical modeling and estimation problems.