Double-Smoothing for Bias Reduction in Local Linear Regression

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 7, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hua He*+ and Li-Shan Huang
• Companies: University of Rochester Medical Center and University of Rochester
• Keywords: local linear regression ; edge effect ; mean squared error ; asymptotic bias ; asymptotic variance

Abstract

Nonparametric local linear regression is commonly used in practice because of its excellent numerical and theoretical properties. It involves fitting a straight line segment over a small region whose midpoint is the abscissa, x, and the predicted value at x is the estimated intercept of that straight line segment.In this paper, we propose a new estimator, the double-smoothing local linear estimator, which combines all fitted local lines in the neighborhood of x with another round of smoothing. The new estimator makes uses of all local intercepts and slopes, in contrast of using only the intercepts in local linear regression. The new estimator reduces the bias to an order of h^4 comparing with h^2 for local linear regression without affecting the order of magnitude of variance. This paper also investigates the edge effects of the proposed new estimator, and simulation results are also given