Asymptotic Theory for Zero Energy Density Estimation with Nonparametric Regression Applications

25 Pages Posted: 21 Jan 2009

See all articles by Qiying Wang

Qiying Wang

University of Sydney

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: January 20, 2009

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.

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

JEL Classification: C14, C22

Suggested Citation

Wang, Qiying and Phillips, Peter C. B., Asymptotic Theory for Zero Energy Density Estimation with Nonparametric Regression Applications (January 20, 2009). Cowles Foundation Discussion Paper No. 1687, Available at SSRN: https://ssrn.com/abstract=1330435

Qiying Wang

University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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