On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models.

DOI10.1016/j.spl.2003.07.018zbMath1103.60040OpenAlexW2076638176MaRDI QIDQ1423023

Enkelejd Hashorva, Frank Miller, Wolfgang Bischoff, Juerg Hüsler

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2003.07.018

zbMATH Keywords

Change-point problemRegression modelsTests of Kolmogorov typeBrownian bridge with trend

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Gaussian processes (60G15) Markov processes: hypothesis testing (62M02)

Related Items (8)

Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test ⋮ Boundary noncrossings of additive Wiener fields ⋮ Boundary non-crossing probabilities for Slepian process ⋮ Asymptotics and bounds for multivariate Gaussian tails ⋮ An Asymptotic Result for Non Crossing Probabilities of Brownian Motion with Trend ⋮ Boundary non-crossing probabilities for fractional Brownian motion with trend ⋮ Regions of alternatives with high and low power for goodness-of-fit tests ⋮ A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend

Cites Work

• Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times
• Limit processes for sequences of partial sums of regression residuals
• Algorithm for the a posteriori detection of multiple changes of a random sequence
• Asymptotics of a boundary crossing probability of a Brownian bridge with general trend
• A functional central limit theorem for regression models
• Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times
• Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test
• Tests for Parameter Instability and Structural Change With Unknown Change Point
• The residual process for non-linear regression
• Asymptotically optimal tests and optimal designs for testing the mean in regression models with applications to change-point problems
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