JSM 2004 - Toronto

Abstract #301687

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Activity Number: 275
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: Business and Economics Statistics Section
Abstract - #301687
Title: Broadening the Scope of the Bootstrap in Complex Problems
Author(s): Manuel A. Dominguez*+ and Victor Aguirre
Companies: ITAM and ITAM
Address: Rio Hondo 1, Mexico City, 01000, Mexico
Keywords: resampling ; Monte-Carlo-based inference ; percentile bootstrap method ; pivotal statistics ; t-ratio
Abstract:

The avaliability of computers has allowed the increase of complexity of models in statistics reach levels never seen before. Computer intensive methods and estimation methods based on simulations to estimate the coefficients of stochastic differential equations are two examples just to name a few. Bootstrap methods are becoming increasingly familiar in statistics. Since these methods are applied by means of Monte Carlo experiments, the computational cost involved in its applicaton to methods like the ones mentioned before could become prohibitive. Therefore, results for reducing this computational cost should be welcome. We propose an approach to the bootstrap that allows us to apply accurate inferential procedures with very small Monte Carlo experiments. Also, the use of this approach permits the determination of the smallest number of bootstrap replications needed to achieve a desired accuracy level. The approach is very general and it applies to the iid or dependent situation. The assumptions required are those that ensure convergence in distribution of bootstrap, there is no need of extra assumptions to insure convergence of moments.

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