## Weaker Conditions to Asymptotic Approximation to L_p-Norms

### by Pablo Martínez-Camblor, Norberto Corral .

Abstract: We derive the asymptotic normality for $L_p$-norms of kernel density estimation under weaker conditions than those requested by Horvath (1991). In particular, the hypothesis (C5) proposed in the referenced paper restricts the useful measurements excluding the Lebesgue measurements to densities with infinite support. In this paper, this hypothesis is weakened and we guarantee the asymptotic normality to $\int|f_n(x)-f(x)|^pdx$\, for an ample variety of densities.

Key Words: Kernel Estimation, KMT process, Lp Norm

Authors:
Pablo Martínez-Camblor, pmcamblor@hotmail.com
Norberto Corral, norbert@uniovi.es

Editor: Coronel-Brizio, Hector F., hcoronel@xal.megared.net.mx

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