In this paper, we propose a minimum projected-distance test for parametric
single-index regression models when the predictors are measured with Berkson errors.
This test asymptotically behaves like a locally smoothing test as if the null model were
with one-dimensional predictor, and is omnibus to detect all global alternative models.
The test can also detect local alternative models that converge to the null model at the
fastest rate that the existing locally smoothing tests with one-dimensional predictor
can achieve. Therefore, the proposed test has potential for alleviating the curse of
dimensionality in this field. We also give two bias-correction methods to center the
test statistic. Numerical studies are conducted to examine the performance of the
proposed test.

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• A minimum projected-distance test for parametric single-index Berkson models