Martingale transforms goodness-of-fit tests in regression models

By Estate V. Khmaladze, Hira L. Koul. 2004

149 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/907dc83490fab0d15a330f30f7e06d510ae5346e

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In Applied Mathematics

In Finance

In Statistics and Probability

Citations in the corpus

Weighted resampling of martingale difference arrays with applications (2011, background): “or rank-statistics, see Khmaladze [18], Khmaladze and Koul [19] or Janssen and Meyer [15].”
Model Checks Using Residual Marked Empirical Processes (2004, methodology): “Usually, different families w deliver different technical approaches for the asymptotic theory, essentially due to the continuity of the family w with respect to the auxiliary parameter x. Compare, for instance, the tightness conditions in Bierens and Ploberger (1997) and Khmaladze and Koul (2004).”
Distribution free specification tests of conditional models (2008, background): “See also Nikabadze and Stute (1997) and Khmaladze and Koul (2004).”
An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “An alternative to bootstrap methods for calibration can be found in the martingale transform of the empirical processes (see Stute et al. 1998b and Khmadladze and Koul 2004), or also in Monte Carlo methods as proposed by Zhu (2005), introducing a randomization of the addends in the i.i.d.…”