Simultaneous Confidence Tubes for Comparison of Several Multivariate Linear Regression Models

TL;DR

This paper extends the methodology of simultaneous confidence bands from univariate to multivariate linear regression models, enabling more informative comparisons among multiple models.

Contribution

It introduces the construction of simultaneous confidence tubes for multivariate regression models, enhancing inference capabilities over traditional hypothesis testing.

Findings

Confidence tubes provide more informative comparisons.

Methodology applied to real examples.

Extension from univariate to multivariate models.

Abstract

Much of the research on multiple comparison and simultaneous inference in the past sixty years or so has been for the comparisons of several population means. Spurrier (1999) seems to be the first to study the multiple comparison of several simple linear regression lines by using simultaneous confidence bands. In this paper, the work of Liu et al. (2004) for finite comparisons of several univariate linear regression models by using simultaneous confidence bands has been extended to finite comparison of several multivariate linear regression models by using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methodologies are illustrated with examples.