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

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

2007-08-14

arxiv.org/abs/0708.1913v1

Annals of Statistics 2007, Vol. 35, No. 2, 815-843

Mathematics

Statistics Theory

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

Scientific paper

10.1214/009053606000001352

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.

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