It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c1 and c2 such that c2≈1.01 c1. A discussion of relative merits of this result versus limit theorems is given.
We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.
Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s -test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics.
En este trabajo se presenta un contraste de normalidad basado en la Energía Informacional de forma paralela al obtenido por Vasicek (1976) basándose en la Entropía de Shannon. Se estima la potencia de este contraste para diversas alternativas comparándola con la de otros contrastes de normalidad. Estos resultados permiten afirmar que este contraste es preferido en algunos casos a algunos contrastes clásicos.
In testing that a given distribution Pbelongs to a parameterized family , one is often led to compare a nonparametric estimateAn of some functional A of P with an element Aθn corresponding to an estimate θn of θ. In many cases, the asymptotic distribution of goodness-of-fit statistics derived from the process n1/2(An−Aθn) depends on the unknown distribution P. It is shown here that if the sequences An and θn of estimators are regular in some sense, a parametric bootstrap approach yields valid approximations...
The paper studies the relations between -divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of -divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary...