Non-classical law of the iterated logarithm behaviour for trimmed sums

Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r _n largest summands are excluded, where r _n=o(log logn). This complements earlier work in which the case log log_n=O(r_n) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732