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September, 1987 Approximating the Distribution of the Maximum Likelihood Estimate of the Change-Point in a Sequence of Independent Random Variables
Yi-Ching Yao
Ann. Statist. 15(3): 1321-1328 (September, 1987). DOI: 10.1214/aos/1176350509

Abstract

The problem of estimating the change-point in a sequence of independent random variables is considered. As the sample sizes before and after the change-point tend to infinity, Hinkley (1970) showed that the maximum likelihood estimate of the change-point converges in distribution to that of the change-point based on an infinite sample. Letting the amount of change in distribution approach 0, it is shown that the distribution, suitably normalized, of the maximum likelihood estimate based on an infinite sample converges to a simple one which is related to the location of the maximum for a two-sided Wiener process. Numerical results show that this simple distribution provides a good approximation to the exact distribution (with an infinite sample) in the normal case. However, it is unclear whether the approximation is good for general nonnormal cases.

Citation

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Yi-Ching Yao. "Approximating the Distribution of the Maximum Likelihood Estimate of the Change-Point in a Sequence of Independent Random Variables." Ann. Statist. 15 (3) 1321 - 1328, September, 1987. https://doi.org/10.1214/aos/1176350509

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0651.62017
MathSciNet: MR902262
Digital Object Identifier: 10.1214/aos/1176350509

Subjects:
Primary: 62E20
Secondary: 62F12

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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