Sur l'approximation de familles de mesures par des familles gaussiennes
type: Item
instance of: scholarly article
title: Sur l'approximation de familles de mesures par des familles gaussiennes
zbMATH Open document ID: 0584.62024
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77258
review text: The local asymptotic theory is often based upon the approximation of a family of measures corresponding to a (not necessarily parametric) model by a Gaussian family. Almost minimal conditions are given to imply the approximability for various distances between experiments, without definitely solving the problem for the strong distance. This long paper didactically presents this theoretical question. It gives general conditions, weaker than the usual LAN ones, and situates the other local asymptotic frameworks. It shows that a Lindeberg condition on square roots of densities is necessary and sufficient in the case of independent, identically distributed variables, and extends results in the case of observations neither independent nor identically distributed, with extra assumptions of asymptotic negligibility of conditional information. Some applications will be provided in a future work.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62B99
zbMATH DE Number: 3936183
zbMATH Keywords: local approximations of families of measures
zbMATH Keywords: non independent, non identically distributed observations
zbMATH Keywords: Gaussian family
zbMATH Keywords: distances between experiments
zbMATH Keywords: strong distance
zbMATH Keywords: Lindeberg condition on square roots of densities
zbMATH Keywords: asymptotic negligibility of conditional information
MaRDI profile type: Publication
author: Lucien Le Cam
description: scientific article; zbMATH DE number 3936183