Title: Switching to the new norm: From heuristics to formal tests using integrable empirical processes
Authors: Tetsuya Kaji - University of Chicago (United States) [presenting]
Abstract: A frequent concern in empirical research is to ensure that a handful of outlying observations have not driven the key empirical findings. We develop new theory of integrable empirical processes and apply it to construct a formal test of outlier robustness. The key is to observe that statistics related to outlier robustness analyses are represented as $L$-statistics-integrals of empirical quantile functions with respect to sample selection measures and to consider these elements in appropriate normed spaces. In particular, we characterize weak convergence of empirical distribution functions and sample selection functions in the space of bounded integrable functions, establish the delta method for empirical quantile functions as integrable functions, and then derive the delta method for $L$-statistics. We also prove the validity of nonparametric bootstrap. An empirical application shows the utility of the proposed test.