Abstract
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.
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