Approximations to the p-values of tests for a change-point under non-standard conditions

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Title: Approximations to the p-values of tests for a change-point under non-standard conditions
Authors: Kelly, Gabrielle E.
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Date: 2016
Abstract: Three test statistics for a change-point in a linear model, variants of those considered by Andrews and Ploberger [Optimal tests when a nusiance parameter is present only under the alternative. Econometrica. 1994;62:1383–1414]: the sup-likelihood ratio (LR) statistic; a weighted average of the exponential of LR-statistics and a weighted average of LR-statistics, are studied. Critical values for the statistics with time trend regressors, obtained via simulation, are found to vary considerably, depending on conditions on the error terms. The performance of the bootstrap in approximating p-values of the distributions is assessed in a simulation study. A sample approximation to asymptotic analytical expressions extending those of Kim and Siegmund [The likelihood ratio test for a change-point in simple linear regression. Biometrika. 1989;76:409–423] in the case of the sup-LR test is also assessed. The approximations and bootstrap are applied to the Quandt data [The estimation of a parameter of a linear regression system obeying two separate regimes. J Amer Statist Assoc. 1958;53:873–880] and real data concerning a change-point in oxygen uptake during incremental exercise testing and the bootstrap gives reasonable results.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Taylor and Francis
Copyright (published version): 2015 Taylor and Francis
Keywords: Change-pointRegressionLikelihood ratio testLagrange multiplier testSup-F testTime trend regressorCorrelated errorsHeteroskedastic errorsSimulationBootstrap
DOI: 10.1080/00949655.2015.1069826
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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