Almost Sure Central Limit Theorems for Heavily Trimmed Sums

Abstract

We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d. random variables with \( E\;X_{1} = 0,\;E\;X^{2}_{1} = 1 \).