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September, 1974 Tests for Change of Parameter at Unknown Times and Distributions of Some Related Functionals on Brownian Motion
Ian B. MacNeill
Ann. Statist. 2(5): 950-962 (September, 1974). DOI: 10.1214/aos/1176342816

Abstract

Statistics are derived for testing a sequence of observations from an exponential-type distribution for no change in parameter against possible two-sided alternatives involving parameter changes at unknown points. The test statistic can be chosen to have high power against certain of a variety of alternatives. Conditions on functionals on $C\lbrack 0,1\rbrack$ are given under which one can assert that the large sample distribution of the test statistic under the null-hypothesis or an alternative from a range of interesting hypotheses is that of a functional on Brownian Motion. We compute and tabulate distributions for functionals defined by nonnegative weight functions of the form $\psi(s) = as^k, k > -2$. The functionals for $-1 \geqq k > -2$ are not continuous in the uniform topology on $C\lbrack 0, 1\rbrack$.

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Ian B. MacNeill. "Tests for Change of Parameter at Unknown Times and Distributions of Some Related Functionals on Brownian Motion." Ann. Statist. 2 (5) 950 - 962, September, 1974. https://doi.org/10.1214/aos/1176342816

Information

Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0289.62059
MathSciNet: MR426253
Digital Object Identifier: 10.1214/aos/1176342816

Subjects:
Primary: 60B10
Secondary: 60E05 , 60G50 , 60H05 , 60J65 , 62E15 , 62E20 , 62F05

Keywords: Bessel functions , exponential family , functionals on Brownian motions , Krhunen-Loeve expansions , Parameter changes at unknown times , stochastic integrals , weak convergence , weight functions

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 5 • September, 1974
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