A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of Their Support

13 Pages Posted: 26 Jan 2016

See all articles by Efstathios Paparoditis

Efstathios Paparoditis

University of Cyprus - Department of Mathematics and Statistics

Dimitris N. Politis

University of California, San Diego (UCSD) - Department of Mathematics

Date Written: March 2016

Abstract

The asymptotic behaviour of nonparametric estimators of the stationary density and of the spectral density function of a stationary process have been studied in some detail in the last 50–60years. Nevertheless, less is known about the behaviour of these estimators when the target function happens to vanish at the point of interest. In the article at hand, we fill this gap and show that asymptotic normality still holds true but with super‐efficient and different rates of convergence for the density and for the spectral density estimators that are affected also by the dependence structure of the process.

Keywords: Central limit theorem, kernel smoothing, nonparametric estimation, overdifferencing, time series

Suggested Citation

Paparoditis, Efstathios and Politis, Dimitris, A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of Their Support (March 2016). Journal of Time Series Analysis, Vol. 37, Issue 2, pp. 182-194, 2016, Available at SSRN: https://ssrn.com/abstract=2722263 or http://dx.doi.org/10.1111/jtsa.12142

Efstathios Paparoditis (Contact Author)

University of Cyprus - Department of Mathematics and Statistics ( email )

P.O. Box 20537
1678 Nicosia
Cyprus
00357-2-338701 (Phone)
00357-2-339061 (Fax)

Dimitris Politis

University of California, San Diego (UCSD) - Department of Mathematics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0112
United States
858-534-5861 (Phone)
858-534-5273 (Fax)

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