Uniformly root-$N$ consistent density estimators for weakly dependent invertible linear processes

Abstract

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate $n^{-1/2}$. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.

Published at http://dx.doi.org/10.1214/009053606000001352 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• On local $U$-statistic processes and the estimation of densities of functions of several sample variables

Cited by in corpus (1)

• Parametric and nonparametric models and methods in financial econometrics