Adaptive nonparametric regression on finite support

Abstract

In this paper, we propose an adaptive nonparametric regression estimation procedure when the covariate is supported over a finite interval. Unlike the classical symmetric kernel regression, the proposed kernel estimator is based on the Beta density function. Its large sample properties, including the asymptotic normality and the uniform convergence, are thoroughly investigated. Meanwhile, general data-driven guidelines for the bandwidth selection are suggested. The finite sample performance of the proposed estimator is evaluated via a simulation study and a real data application.

KEYWORDS:

• Kernel smoothing
• Beta kernel regression
• boundary effects
• consistency and asymptotic normality

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62G08
• 62G20