Convergence in distribution of lightly trimmed and untrimmed sums are equivalent
Harry Kesten · Mathematical Proceedings of the Cambridge Philosophical Society · 1993
Abstract We show that trimming a fixed number of terms from sums of i.i.d. random variables (so-called light trimming) can have only a modest effect on limiting behaviour. More specifically, the trimmed sums, after centralization and normalization, have a limit distribution, if and only if the untrimmed sums have a limit distribution (with the same centralization and normalization constants).