Testing with a nuisance parameter present only under the alternative

What is it about?

The paper discusses a Score-type statistic to test for a null hypothesis with "vanishing parameters", namely parameters which only the null hypothesis get undefined.

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Why is it important?

We have presented a simple and poweful approach for hypothesis testing with a nuisance parameter present only under the alternative. Unlike proposals relying on simulations and non-standard null distributions, the proposed statistic allows to get p-value through the usual Normal of Chi-squared distributions.