The estimating function bootstrap

TL;DR: In this article, the authors propose a bootstrap procedure which estimates the distribution of an estimating function by resampling its terms using bootstrap techniques, which can be applied to a wide class of practical problems where data are independent but not necessarily identically distributed.

Abstract: The authors propose a bootstrap procedure which estimates the distribution of an estimating function by resampling its terms using bootstrap techniques. Studentized versions of this so-called estimating function (EF) bootstrap yield methods which are invariant under reparametrizations. This approach often has substantial advantage, both in computation and accuracy, over more traditional bootstrap methods and it applies to a wide class of practical problems where the data are independent but not necessarily identically distributed. The methods allow for simultaneous estimation of vector parameters and their components. The authors use simulations to compare the EF bootstrap with competing methods in several examples including the common means problem and nonlinear regression. They also prove symptotic results showing that the studentized EF bootstrap yields higher order approximations for the whole vector parameter in a wide class of problems. Les auteurs proposent une procedure bootstrap qui estime la loi d'une fonction d'estimation en reechantillonnant ses termes au moyen de techniques d'auto-amorcage. Les versions studentisees de ce bootstrap dit de la fonction d'estimation (FE) conduisent a des methodes invariantes par reparametrisation. Cette approche, qui s'avere souvent plus rapide et plus precise que les methodes bootstrap traditionnelles, s'applique a de tres nombreuses situations concretes ou les observations sont independantes mais pas necessairement de měme loi. Elle permet l'estimation simultanee de plusieurs parametres vectoriels et de leurs composantes. Les auteurs presentent des simulations permettant de comparer le bootstrap FE a ses competiteurs dans difterents contextes, notamment celui de la regression non lineaire et du probleme des moyennes communes. Us demontrent egalement des resultats asymptotiques prouvant que dans beaucoup de situations, le bootstrap FE studentise fournit une meilleure approximation du vecteur des parametres.