Confidence regions in semilinear regression

Abstract

SUMMARY

For the simple semilinear regression model.y =βf(θ) +ɛ, we obtain conservative approximations to likelihood ratio confidence regions for 6 and joint regions for (θ,β) which in many cases are essentially exact. To approximate the required probability we adapt the upcrossings approach of Johnstone & Siegmund (1989). In simple examples we compare our regions with two others which have been widely discussed in the literature.