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Asymptotic Theory for Zero Energy Density Estimation with Nonparametric Regression Applications

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Abstract

A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya-Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1687.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1687.

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Length: 24 pages
Date of creation: Jan 2009
Date of revision:
Publication status: Published in Econometric Theory (2011), 27(2): 235-259
Handle: RePEc:cwl:cwldpp:1687

Note: CFP 1319
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Related research

Keywords: Brownian local time; Cointegration; Integrated process; Local time density estimation; Nonlinear functionals; Nonparametric regression; Unit root; Zero energy functional;

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  1. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 143-164, February.
  2. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  3. P. Jeganathan, 2008. "Limit Theorems for Functionals of Sums that Converge to Fractional Brownian and Stable Motions," Cowles Foundation Discussion Papers 1649, Cowles Foundation for Research in Economics, Yale University.
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