Confidence intervals for lognormal regression and a non-parametric alternative

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.