Universiteit Utrecht

Department of Mathematics


Abstract


On asymptotic expansion of pseudovalues in nonparametric median regression
Eduard Belitser (UU), Februari 12, 2003

We consider the median regression model, where the distribution of the noise is assumed to be unknown, with zero median and satisfying some weak conditions. Possible noise distributions may have heavy tails, so that, for example, no moments of the noises exist. Therefore, traditional estimation methods (for example, kernel methods) can not be applied directly in this situation.

On the basis of a preliminary estimator, we construct certain variables called Tukey's pseudovalues which do not depend on the noise distribution. We derive an asymptotic expansion for this variables, which mimics the nonparametric regression model with binary noises. In so doing, we reduce our original observation model with ``bad'' (heavy-tailed) noises effectively to the nonparametric regression model with ``nice'' (binary) noises.


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Martijn Pistorius (pistorius@math.uu.nl)