@article{Bernshtein1981AsymptoticallySC,
title={Asymptotically similar criteria},
author={A. V. Bernshtein},
journal={Journal of Soviet Mathematics},
year={1981},
volume={17},
pages={1825-1857}
}

Works are discussed on testing composite statistical hypotheses with parameters by means of criteria which asymptotically preserve a constant level of significance for all values of the nuisance parameters. Criteria of the likelihood ratio, criteria based on estimates of all parameters, asymptotically similar criteria of goodness of fit, and the C(α)-criteria of Neyman are considered in detail.