Title

Asymptotic Theory for Zero Energy Density Estimation with Nonparametric Regression Applications

Document Type

Discussion Paper

Publication Date

1-1-2009

CFDP Number

1687

CFDP Pages

26

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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