- Volume 10, Number 4 (2004), 721-752.
The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator
Let denote a kernel estimator of a density f in such that for some p>2. It is shown, under quite general conditions on the kernel K and on the window sizes, that the centred integrated squared deviation of from its mean, satisfies a law of the iterated logarithm (LIL). This is then used to obtain an LIL for the deviation from the true density, . The main tools are the Komlós-Major-Tusnády approximation, a moderate-deviation result for triangular arrays of weighted chi-square variables adapted from work by Pinsky, and an exponential inequality due to Giné, Latała and Zinn for degenerate U-statistics applied in combination with decoupling and maximal inequalities.
Bernoulli, Volume 10, Number 4 (2004), 721-752.
First available in Project Euclid: 23 August 2004
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Giné, Evarist; Mason, David M. The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator. Bernoulli 10 (2004), no. 4, 721--752. doi:10.3150/bj/1093265638. https://projecteuclid.org/euclid.bj/1093265638