MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models
Mohammed Kadi Attouch and Tawfik Benchikh

Abstract

We propose a family of robust nonparametric estimators for robust regression function based on k-nearest neighbour (k-NN) method. We establish the asymptotic normality of the estimator under the concentration properties on small balls of the probability measure of the functional explanatory variables.

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Keywords: Asymptotic distribution; functional data; k-nearest neighbour; robust estimation; small balls probability.

MSC: 62G05, 62G08, 62G20, 62G35

Pages:  275--285     

Volume  64 ,  Issue  4 ,  2012