Inference on many jumps in nonparametric panel regression models

We investigate the significance of change-points within fully nonparametric regression contexts, with a particular focus on panel data where data generation processes vary across units, and error terms may display complex dependency structures. In our setting the threshold effect depends on one specific covariate, and we permit the true nonparametric regression to vary based on additional (latent) variables. We propose two uniform testing procedures: one to assess the existence of change-points and another to evaluate the uniformity of such effects across units. Our approach involves deriving a straightforward analytical expression to approximate the variance-covariance structure of change-point effects under general dependency conditions. Notably, when Gaussian approximations are made to these test statistics, the intricate dependency structures within the data can be safely disregarded owing to the localized nature of the statistics. This finding bears significant implications for obtaining critical values. Through extensive simulations, we demonstrate that our tests exhibit excellent control over size and reasonable power performance in finite samples, irrespective of strong cross-sectional and weak serial dependency within the data. Furthermore, applying our tests to two datasets reveals the existence of significant nonsmooth effects in both cases.