A functional central limit theorem for regression models

DOI10.1214/aos/1024691248zbMath0936.62072OpenAlexW1982629204MaRDI QIDQ1807139

Wolfgang Bischoff

Publication date: 9 November 1999

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1024691248

zbMATH Keywords

functional central limit theoremchange-point problemsregression residualspartial sums processesfunctions of Brownian motion

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Linear regression; mixed models (62J05) Design of statistical experiments (62K99) Functional limit theorems; invariance principles (60F17)

Related Items (12)

Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test ⋮ THE CHOICE OF A REGRESSION MODEL OF THE BODY WEIGHT ON THE HEIGHT VIA AN EMPIRICAL BRIDGE ⋮ Asymptotics of sums of regression residuals under multiple ordering of regressors ⋮ Partial sum process to check regression models with multiple correlated response: with an application for testing a change-point in profile data ⋮ On detecting alternatives by one-parametric recursive residuals ⋮ Optimal designs which are efficient for lack of fit tests ⋮ 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. ⋮ Asymptotic theory in model diagnostic for general multivariate spatial regression ⋮ \(L_p\)-approximable sequences of vectors and limit distribution of quadratic forms of random variables ⋮ Remarks on invariance principle for one-parametric recursive residuals ⋮ Bayesian optimal design for changepoint problems ⋮ Asymptotics of an empirical bridge of regression on induced order statistics

Cites Work

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• An optimal experimental design for the haar regression model
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• Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time
• Asymptotically optimal tests and optimal designs for testing the mean in regression models with applications to change-point problems

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