Edgeworth expansions for two-stage sampling with applications to stratified and cluster sampling

A two-term Edgeworth expansion for the standardized version of the sample total in a two-stagesampling design is derived. In particular, for the commonly used stratified and cluster sampling schemes,formal two-term asymptotic expansions are obtained for the Studentized versions of the sample total. Theseresults are applied in conjunction with the bootstrap to construct more accurate confidence intervals for theunknown population total in such sampling schemes.Les auteurs pr´esentent un d´eveloppement en deux termes d’une s´erie d’Edgeworth pour l’estimateurdu total bas´e sur un plan ´echantillonnal `a deux phases. Ils obtiennent en particulier des d´eveloppementsasymptotiques formels pour la version studentis´ee du total ´echantillonnal bas´e sur un ´echantillonnage stratifi´eet sur un ´echantillonnage en grappes. Les auteurs utilisent ces r´esultats et des m´ethodes de r´e´echantillonnageafin de construire des intervalles de confiance plus pr´ecis pour le total de la population dans le contexte deces plans d’´echantillonnage.Statistical methods for ecological research on data from national monitoring programs. Funded by the Swedish Research Council. Grant Number 340-2013-5076

Tests of fit using spacings statistics with estimated parameters

Let X1,..., Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Relative to this unknown distribution function suppose one would like to test a null hypothesis concerning the goodness of fit of F to some distribution function using symmetric functions of sample spacings. In some applications the null hypothesis is simple while in others it may be composite. In this article we present the large sample theory of tests based on symmetric functions of sample spacings under composite null hypotheses and contiguous alternatives. It is shown that these test statistics have the same asymptotic distribution in the case when parameters must be estimated from the sample as in the case when parameters are specified. Optimal goodness of fit tests are also constructed for these hypotheses.Spacings tests goodness of fit tests nuisance parameters optimal tests Pitman efficiency