Adam Lee: Locally robust and efficient tests for non-regular semiparametric models
This paper considers hypothesis testing in semiparametric models which may be non – regular for certain values of a (potentially infinite dimensional) nuisance parameter. In such models no (locally) regular estimator of the parameter of interest exists. The situation for testing is somewhat different: I establish that C(α) – style test statistics achieve their limiting distributions in a (locally) regular manner under mild conditions, leading to tests with correct size in situations where standard tests fail to control size. Additionally, I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the case where the efficient information matrix is singular. This permits the generalisation of classical power bounds to the non – regular case. I provide appropriate statements of these bounds and give conditions under which they are attained by the proposed C(α) – style tests. Three examples are worked out in detail.
Adam is an Assistant Professor in the Department of Data Science & Analytics at BI Norwegian Business School. Adam has research interests in econometric \& statistical theory, semiparametric models, time series, and non-asymptotic statistics. Prior to coming to Oslo, Adam, took a PhD at Universitat Pompeu Fabra, Spain. And before that he worked as a research assistant at Princeton university.
Published Nov. 14, 2023 1:18 PM
- Last modified Nov. 14, 2023 1:20 PM