Finding extrema and zeros in nonparametric regression when the data contains outliers

Abstract

The estimation of extrema and zeros in robust nonparametric regression is investigated. Rates of weak uniform convergence of the estimates to the true extremum (or zero) are given. These rates are found to be comparable to the rates of convergence of the extremum and zero estimates given by Müller (1988, Chapter 8) in ordinary smoothing. Finally, asymptotic normality of the estimates is established.

Keywords:

• Nonparametric regression
• robust smoother
• kernel, bandwidth