Title: Weak convergence of the least concave majorant of estimators for a concave distribution function
Authors: Brendan Beare - University of California, San Diego (United States) [presenting]
Zheng Fang - Kansas State University (United States)
Abstract: The asymptotic behavior of the least concave majorant of an estimator of a concave distribution function is studied under general conditions. In particular, we allow the true concave distribution function to violate strict concavity, so that the empirical distribution function and its least concave majorant are not asymptotically equivalent. We also allow for serially dependent data and a distribution with potentially unbounded support on the nonnegative half-line. Our results are proved by demonstrating the Hadamard directional differentiability of the least concave majorant operator. While the standard bootstrap fails, we show that the rescaled bootstrap of Dumbgen can deliver valid inference.