Abstract

MARTINEZ-CAMBLOR, PABLO; CORRAL, NORBERTO  and  LOPEZ, TERESA. Cramér-Chernoff Theorem for L₁-norm in Kernel Density Estimator for Two Independent Samples. Rev.Colomb.Estad. [online]. 2009, vol.32, n.2, pp.289-299. ISSN 0120-1751.

In this paper a Chernoff type theorem for the L₁ distance between kernel estimators from two independent and identically distributed random samples is developed. The harmonic mean is used to correct the distance for inequal sample sizes case. Moreover, the proved result is used to compute the Bahadur slope of a test based on L₁ distance and to compare it with the classical nonparametric Mann-Whitney test by using the Bahadur relative efficiency.

Keywords : Kernel estimator; Large deviation; Bahadur slope.

        · abstract in English     · text in Spanish     · Spanish ( pdf )