Asymptotic behavior of trimmed sums (Q2888807)

Basic results in the central limit theory of moderately trimmed sums are firstly reviewed. One theorem yields a randomized functional central limit theorem (CLT) for the modulus trimmed sums in the domain of attraction of a stable law, but it does not say when the ordinary nonrandom CLT holds. Other theorems also give a picture on the CLT for modulus trimmed sums, but their statistical application is difficult. It is impossible to decide from a sample if the underlying distribution satisfies the required conditions.