Martingale Transforms Goodness-of-Fit Tests in Regression Models
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...
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| Veröffentlicht in: | The Annals of statistics 2004-06, Vol.32 (3), p.995-1034 |
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| container_end_page | 1034 |
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| container_title | The Annals of statistics |
| container_volume | 32 |
| creator | Khmaladze, Estate V. Koul, Hira L. |
| description | 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. |
| doi_str_mv | 10.1214/009053604000000274 |
| format | Article |
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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. 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 62G10 62J02 Approximation Asymptotically distribution free Brownian bridge Brownian motion Distribution functions Distribution theory Estimators Exact sciences and technology General topics Linear regression Martingales Mathematical models Mathematics Monte Carlo simulation Nonparametric inference partial sum processes Partial sums Probability and statistics Probability theory and stochastic processes Regression analysis Sample size Sciences and techniques of general use Statistics Stochastic processes Testing |
| title | Martingale Transforms Goodness-of-Fit Tests in Regression Models |
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