Corrected confidence intervals based on the signed root transformation for multi-parameter sequentially designed experiments

•A very general two-parameter adaptive model is studied.•Corrected confidence intervals are constructed for the parameter of interest.•Very weak expansions are used to obtain the correction terms.•Simulation shows that the approximations are quite accurate.•The confidence interval approach extends to higher dimensions.

A two-parameter model is studied in which there is a parameter of interest and a nuisance parameter. Corrected confidence intervals are constructed for the parameter of interest for data from a sequentially designed experiment. This is achieved by considering the distribution of the first component of the bivariate signed root transformation, and then by applying a version of Stein's identity and very weak expansions to determine the correction terms. The accuracy of the approximations is assessed by simulation for three nonlinear regression models with normal errors, a two-population normal model, a logistic model and a Poisson model. An extension of the approach to higher dimensions is briefly discussed.