On The Behavior Of Nonparametric Density And Spectral Density Estimators At Zero Points Of Their Support
AbstractThe asymptotic behavior of nonparametric estimators of the probability density function of an i.i.d. sample and of the spectral density function of a stationary time series have been studied in some detail in the last 50-60 years. Nevertheless, an open problem remains to date, namely the behavior of the estimator when the target function happens to vanish at the point of interest. In the paper at hand we fill this gap, and show that asymptotic normality still holds true but with a super-efficient rate of convergence. We also provide two possible applications where these new results can be found useful in practice.
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Date of creation: 01 Dec 2012
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Social and Behavioral Sciences; Nonparametric Density;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-07 (All new papers)
- NEP-ECM-2013-01-07 (Econometrics)
- NEP-ETS-2013-01-07 (Econometric Time Series)
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- Politis, D N & McElroy, Tucker S, 2009.
"Fixed-b asymptotics for the studentized mean from time series with short, long or negative memory,"
University of California at San Diego, Economics Working Paper Series
qt70c4x0sq, Department of Economics, UC San Diego.
- McElroy, Tucker & Politis, Dimitris N., 2012. "Fixed-B Asymptotics For The Studentized Mean From Time Series With Short, Long, Or Negative Memory," Econometric Theory, Cambridge University Press, vol. 28(02), pages 471-481, April.
- Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1218-1245, August.
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