2004/05/27 by Estáte V. Khmaladze, Estate V. Khmaladze, Hira L. Koul · 2 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Financial Risk and Volatility Modeling #Statistical and numerical algorithms #math.ST #msc:62G10 #msc:62J02. #stat.TH
paper · pdf · doi:10.1214/009053604000000274
published as Annals of Statistics 2004, Vol. 32, No. 3, 995-1034
openalex publication_date 2004/05/27 · arxiv created 2004/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.