Moderate deviations for the $L_1$-norm of kernel density estimators

Andrei Yu. Zaitsev

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arXiv · 1805.01770

Moderate deviations for the $L_1$-norm of kernel density estimators

Andrei Yu. Zaitsev

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Abstract

The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are estimated. By assumption, the density tends to zero as a power-type function when the argument tends to infinity. Moreover, the density may have a finite number of power-type zeroes and of points with power-type tending to infinity. For such densities the size of zones of moderate deviations are found.

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Andrei Yu. Zaitsev. 2018-05-02. Moderate deviations for the $L_1$-norm of kernel density estimators. https://arxiv.org/abs/1805.01770

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