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June 2004 Martingale transforms goodness-of-fit tests in regression models
Estate V. Khmaladze, Hira L. Koul
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Ann. Statist. 32(3): 995-1034 (June 2004). DOI: 10.1214/009053604000000274


This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model when the error distribution is unknown. For the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes. The advantage of this transform is that the corresponding tests are asymptotically distribution free. For the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms. A Monte Carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes.


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Estate V. Khmaladze. Hira L. Koul. "Martingale transforms goodness-of-fit tests in regression models." Ann. Statist. 32 (3) 995 - 1034, June 2004.


Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1092.62052
MathSciNet: MR2065196
Digital Object Identifier: 10.1214/009053604000000274

Primary: 62G10
Secondary: 62J02

Keywords: asymptotically distribution free , partial sum processes

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 3 • June 2004
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