Confidence Bands in Multivariate Polynomial Regression

Abstract

This paper deals with the problem of constructing a confidence band over the real line for a polynomial regression curve of known degree. The situation involves successive, and therefore in general, correlated measurements, say, in time, on the same objects. Two methods for constructing these bands are developed when the measurements are assumed to be multivariate normal. They are then compared to determine when one provides narrower bandwidths than the other. The confidence level I – α is, in general, a lower bound.

KEY WORDS:

• Confidence bands
• Polynomial regression
• Arbitrary known degree
• Multivariate normal observations