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   -> Volume 4, Issue 2


Preprint: Monte Carlo Variance of Scrambled Equidistrib. Quadrature
 
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Art Owen
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PostPosted: Mon Dec 02, 2002 5:42 pm    
Subject: Preprint: Monte Carlo Variance of Scrambled Equidistrib. Quadrature
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Preprint: Monte Carlo Variance of Scrambled Equidistrib. Quadrature

Preprint: Monte Carlo Variance of Scrambled Equidistribution Quadrature
Author: Art B. Owen

Correspondence: Dept of Statistics
Sequoia Hall
Stanford CA 94305

art@playfair.stanford.edu

Abstract:

A method of numerical integration over the high dimensional
unit cube is studied. The method combines equidistribution methods
and Monte Carlo, attaining the accuracy of the former, while
allowing error estimation through replication.

The relevance to wavelets is as follows: the integrand is
first written in a multivariate base b Haar resolution. The
coarsest terms are integrated exactly. Higher order terms
make a contribution to the sampling variance of the estimated
integral.

Along a judiciously chosen sequence for the number of evaluations
n, the variance of the estimate is o(1/n), as compared to the
usual O(1/n).


Availability:

By anonymous ftp or WWW from playfair.stanford.edu. Look
under technical reports, then under author = Owen.
All times are GMT + 1 Hour
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