Data sharpening method in regression confidence band

Abstract

The confidence band of functions is complicated by the over-smoothing problem and the residual distribution. In this paper, we use bootstrap and data-sharpening methods to establish a general confidence band. The construction is simple and the band is narrower than existing estimation methods. At the same time, a technique based on quantiles makes the confidence band more controllable and damps down the stochastic error term. Afterwards, we conduct a limited simulation to illustrate that the proposed band performs better than existing ones. Finally, we show the theoretical properties of the results and prove them.

Keywords:

• Confidence band
• nonparametric
• data sharpening
• kernel method
• bootstrap