Large and moderate deviations principles for kernel estimators of the multivariate regression

Details Large and moderate deviations principles for kernel estimators of the multivariate regression Large and moderate deviations principles for kernel estimators of the multivariate regression

2007-03-12

arxiv.org/abs/math/0703341v1

Mathematics

Statistics Theory

31 pages

Scientific paper

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the unidimensional case for the Nadaraya-Watson estimator. Moreover, we give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.

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