Some uniform large deviation results in nonparametric function estimation

Sidi Maouloud

Journal of Nonparametric Statistics, 2008, vol. 20, issue 2, 129-152

Abstract: In this paper, we investigate large deviation asymptotics involving classes of nonparametric estimates. We introduce a random process, say Zn, which allows to derive, using the contraction principle, results for several nonparametric estimates from the large deviations principle stated for Zn. The usual examples of nonparametric estimates include the histogram density estimate as well as the regressogram. Note that uniform behaviours over classes of density and regression functions as well as over classes of their estimates have been considered.

Date: 2008
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DOI: 10.1080/10485250801908389

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