  In various applications of regression analysis, in addition to errors in the
dependent observations also errors in the predictor variables play a
substantial role and need to be incorporated in the statistical modeling
process. In this paper we consider a nonparametric measurement error model of
Berkson type with fixed design regressors and centered random errors, which is
in contrast to much existing work in which the predictors are taken as random
observations with random noise. Based on an estimator that takes the error in
the predictor into account and on a suitable Gaussian approximation, we derive
%uniform confidence statements for the function of interest. In particular, we
provide finite sample bounds on the coverage error of uniform confidence bands,
where we circumvent the use of extreme-value theory and rather rely on recent
results on anti-concentration of Gaussian processes. In a simulation study we
investigate the performance of the uniform confidence sets for finite samples.
