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Schick, Anton; Wefelmeyer, Wolfgang

Uniformly root-\(n\) consistent density estimators for weakly dependent invertible linear processes. (English) Zbl 1117.62036

Ann. Stat. 35, No. 2, 815-843 (2007).
Summary: 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.

Cited in 20 Documents

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

least squares estimator; kernel estimator; plug-in estimator; functional limit theorem; infinite-order moving average process; infinite-order autoregressive process
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References:

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