Showing papers by "Miguel A. Arcones published in 1991"

Additions and correction to “The bootstrap of the mean with arbitrary bootstrap sample”

Abstract: Some inaccuracies in [2] are corrected and some additional results are presented. The bootstrap central limit theorem in the domain of attraction case is improved to include convergence of bootstrap moments. Self-normalized limit theorems for variables in the domain of attraction of a p-stable law are bootstrapped, thus freeing the bootstrap from the index p and the norming constants {bn}. Simultations on the bootstrap of the self-normalized sums for a few values of p and n are also included. RESUME. Nous corrigeons quelques inexactitudes de l’article [2] et nous présentons certains resultats complementaires. Nous ameliorons le théorème central limite « bootstrap » pour obtenir la convergence des moments « bootstrap ». Des theoremes limites auto-normalises pour des variables dans le domaines d’attraction d’une loi p-stable sont donnes sous forme bootstrap, ce qui libere le bootstrap de l’indice p et des constantes de normalisation (bn). On presente aussi des simulations du bootstrap des sommes auto-normalisee pour quelques valeurs de p et n. (*) Research partially supported by N.S.F. grant No. DMS-9000132 and PSC-CUNNY grant No. 661376. Annales de l’lnstitut Henri Poincaré Probabilités et Statistiques 0246-0203 Vol. 27/91/04/583i 13’~ 330/0 Gauthier-Villars 584 M. A. ARCONES AND E. GINÉ

Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions

Abstract: The Kolmogorov distance between the empirical $\operatorname{cdf} F_n$ and its symmetrization $sF_n$ with respect to an adequate estimator of the center of symmetry of $P$ is a natural statistic for testing symmetry. However, its limiting distribution depends on $P$. Using critical values from the symmetrically bootstrapped statistic (where the resampling is made from $sF_n$) produces tests that can be easily implemented and have asymptotically the correct levels as well as good consistency properties. This article deals with the asymptotic theory that justifies this procedure in particular for a test proposed by Schuster and Barker. Because of lack of smoothness (in some cases implying non-Gaussianness of the limiting processes), these tests do not seem to fall into existing general frameworks.