Working Papers
Understanding regression shape changes through nonparametric testing, with Tatiana Komarova.
We propose a procedure for testing whether a nonparametric regression mean satisfies a shape restriction that varies within the domain of the regressor. Notably, the change points of these shape restrictions are unknown and must be estimated. Our test statistic is based on the empirical process, drawing inspiration from Khmaladze (1982). This paper extends the nonparametric methodology of Komarova and Hidalgo (2023) by proposing a method to estimate the shape change points and consequently addressing the additional estimation errors introduced by that stage. We analyse strategies for managing these errors and adapting the testing approach accordingly. Our framework accommodates various common shapes, such as (inverse) U-shapes, S-shapes, and W-shapes. Furthermore, our method is applicable to partial linear models, thereby encompassing a broad spectrum of applications. We demonstrate the efficacy of our approach through application to several economic problems and data.
Testing for additivity in nonparametric regression models, with Javier Hidalgo and Tatiana Komarova.
We describe and examine a test for additivity in a nonparametric framework using partial sums empirical processes.