Robust confidence interval for a residual standard deviation

Abstract

The residual standard deviation of a general linear model provides information about predictive accuracy that is not revealed by the multiple correlation or regression coefficients. The classic confidence interval for a residual standard deviation is hypersensitive to minor violations of the normality assumption and its robustness does not improve with increasing sample size. An approximate confidence interval for the residual standard deviation is proposed and shown to be robust to moderate violations of the normality assumption with robustness to extreme non-normality that improves with increasing sample size.

Keywords:

• Dispersion
• regression
• model fit

Acknowledgement

This material is based upon work supported by the National Science Foundation under Grant No. 0343552.