Moderate deviation principle in nonlinear bifurcating autoregressive models

Abstract

Recently, nonparametric techniques have been proposed to study bifurcating autoregressive processes. One can build Nadaraya–Watson type estimators of the two autoregressive functions as in Bitseki Penda et al. (2017) and Bitseki Penda and Olivier (2017). In the present work, we prove moderate deviation principle for these estimators.