Comparison of simultaneous confidence bands for univariate polynomial regression over an interval

Abstract

This article compares confidence bands for univariate polynomial regressions over an interval constraint. The competing methods are those from Naiman (1986), Sun and Loader (1994), and Liu et al. (2008), respectively. They are compared in terms of critical values under various designs. It is found that Sun’s bands can be somewhat narrower or much wider than Liu’s bands that underlines the fact that Sun’s bands are approximate and so can be both liberal or conservative while Liu’s bands are exact when the number of simulations is large enough. Naiman’s bands are conservative but can be substantially wider than Liu’s bands.

Keywords:

• Simultaneous confidence bands
• Polynomial regression
• Critical value

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F30, 62J05.

Additional information

Funding

This research work was supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China (No. 11201059).