Universal asymptotic normality for conditionally trimmed sums

The conditionally trimmed sums formed from an arbitrary i.i.d. sample are shown to satisfy both a probabilistic and empirical central limit theorem with a normal limit law. The specific method of trimming attempts to retain as many summands as possible and deletes only terms of sufficient magnitude. The behavior of the deleted terms is also studied for random variables which generate affinely stochastically compact partial sums.asymptotic normality trimmed sums extreme values