Confidence intervals for lognormal regression and a non-parametric alternative

Abstract

Approximate confidence intervals are given for the lognormal regression problem. The error in the nominal level can be reduced to O(n ⁻²), where n is the sample size. An alternative procedure is given which avoids the non-robust assumption of lognormality. This amounts to finding a confidence interval based on M-estimates for a general smooth function of both ϕ and F, where ϕ are the parameters of the general (possibly nonlinear) regression problem and F is the unknown distribution function of the residuals. The derived intervals are compared using theory, simulation and real data sets.

Keywords:

• confidence interval
• lognormal
• m-estimate
• non-parametric
• regression

AMS 2000 Subject Classifications :

• Primary: 62F25
• Secondary: 62G15

Acknowledgements

The authors would like to thank the editor and the associate editor for careful reading and for their comments which greatly improved the paper.