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.