Schick, Anton et Wefelmeyer, Wolfgang, Uniformly Root-N Consistent Density Estimators for Weakly Dependent Invertible Linear Processes, Annals of statistics , 35(2), 2007, pp. 815-843
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.