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June, 1994 Lattice Sampling Revisited: Monte Carlo Variance of Means Over Randomized Orthogonal Arrays
Art Owen
Ann. Statist. 22(2): 930-945 (June, 1994). DOI: 10.1214/aos/1176325504

Abstract

Randomized orthogonal arrays provide good sets of input points for exploration of computer programs and for Monte Carlo integration. In 1954, Patterson gave a formula for the randomization variance of the sample mean of a function evaluated at the points of an orthogonal array. That formula is incorrect for most of the arrays that are practical for computer experiments. In this paper we correct Patterson's formula. We also remark on a defect, related to coincidences, in some orthogonal arrays. These are arrays of the form $OA(2q^2, 2q + 1, q, 2)$, where $q$ is a prime power, obtained by constructions due to Bose and Bush and to Addelman and Kempthorne. We conjecture that subarrays of the form $OA(2q^2, 2q, q, 2)$ may be constructed to avoid this defect.

Citation

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Art Owen. "Lattice Sampling Revisited: Monte Carlo Variance of Means Over Randomized Orthogonal Arrays." Ann. Statist. 22 (2) 930 - 945, June, 1994. https://doi.org/10.1214/aos/1176325504

Information

Published: June, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0807.62059
MathSciNet: MR1292549
Digital Object Identifier: 10.1214/aos/1176325504

Subjects:
Primary: 62K15
Secondary: 05B15, 65C05, 65D30

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 2 • June, 1994
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