ASYMPTOTIC THEORY FOR ZERO ENERGY FUNCTIONALS WITH NONPARAMETRIC REGRESSION APPLICATIONS

By Qiying Wang, Peter C. B. Phillips. Econometric Theory, 2010

51 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/77cfe1238396cbb8e6fff3ffac806ef5fe38ebf2

Citations in the corpus

• Estimating Smooth Structural Change in Cointegration Models (2017, unknown): “…used local polynomial smoothing method in practical work and has certain advantages over local level regression in stationary regression, although Wang and Phillips (2009b, 2011, 2015) showed that such bias reduction with local linear methods does not occur (and hence is not an advantage) in…”
• Nonparametric Predictive Regression (2015, unknown): “…varying computation times of the same order of magnitude. hn = 1/ ln(ln(n)) and data determined bandwidth ĥn = n − 1 5 m̂− 12 where m̂ is the localWhittle estimator (e.g. Robinson, 1995) for the parameter m.12 The last two bandwidths are optimal in the Wang and Phillips (2011) sense.”