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arXiv · 2403.05999

Locally Regular and Efficient Tests in Non-Regular Semiparametric Models

Adam Lee
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Abstract

This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C($α$) style tests are locally regular under mild conditions, including in cases where locally regular estimators do not exist, such as models which are (semiparametrically) weakly identified. I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the non-regular case and generalise classical power bounds to this case. I give conditions under which these power bounds are attained by the proposed C($α$) style tests. The application of the theory to a single index model and an instrumental variables model is worked out in detail.

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Adam Lee. 2024-12-20. Locally Regular and Efficient Tests in Non-Regular Semiparametric Models. https://arxiv.org/abs/2403.05999

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