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Moderate deviations principle for the kernel estimator of nonrandom regression functions. (English. French summary) Zbl 1358.62042

Summary: The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of confidence regions for the regression function.

MSC:

62G08 Nonparametric regression and quantile regression
62G07 Density estimation
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
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Full Text: Euclid