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.
Brownian Local time, Cointegration, Integrated process, Local time density estimation, Nonlinear functionals, Nonparametric regression, Unit root, Zero energy functional
Cambridge University Press (CUP): HSS Journals
WANG, Qiying and Peter C. B. PHILLIPS.
Asymptotic Theory for Zero Energy Functionals with Nonparametric Regression Applications. (2011). Econometric Theory. 27, (2), 235-259. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1822
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