Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 1, 55--86

Robust Jump Detection in Regression Surface

Tim Garlipp and Christine H. M\"{u}ller, Fachbereich Mathematik, Universit\"{a}t Kassel, Germany

SUMMARY. We use the difference of two asymmetric M-kernel estimators to detect jumps in two-dimensional regression functions. The method extends and corrects the Rotational Difference Kernel Estimator method proposed by Qiu (1997). For regression functions with only one explicit jump curve and additive noise, we show consistency for the jump location and height. In a simulation study, the consistency is also demonstrated for the case that $30\%$ of the observations are replaced by outliers. In this case, the robust M-kernel estimators are superior to the classical kernel-estimators.

AMS (2000) subject classification. 62G20, 62G35, 62G08, 62G05, 62H35.

Key words and phrases. M-kernel estimation, consistency, edge detection, jump regression function, robustness against outliers.

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