2024/03/09 by Lee, Adam
#Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2403.05999
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.