Asymptotic theory for local estimators based on Bregman divergence

Abstract

AbstractThis article is concerned with asymptotic theory for local estimators based on Bregman divergence. We consider a localized version of Bregman divergence induced by a kernel weight and minimize it to obtain the local estimator. We provide a rigorous proof for the asymptotic consistency of the local estimator in a situation where both the sample size and the bandwidth involved in the kernel weight increase. Asymptotic normality of the local estimator is also developed under the same asymptotic scenario. Monte Carlo simulations are also performed to confirm the theoretical results. The Canadian Journal of Statistics 47: 628–652; 2019 © 2019 Statistical Society of Canada