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Locally Regular and Efficient Tests in Non-Regular Semiparametric Models

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  • Adam Lee

Abstract

This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C($\alpha$) 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($\alpha$) 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. "Locally Regular and Efficient Tests in Non-Regular Semiparametric Models," Papers 2403.05999, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2403.05999
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