Asymptotic Behavior of Self-Normalized Trimmed Sums: Nonnormal Limits III

Abstract

Let X,X ₁,X ₂,…, be independent, identically distributed real random variables which are symmetric about the origin and have common nondegenerate distribution function F. Arrange the random sample X ₁,X ₂},…, X _n in decreasing order of magnitude, breaking ties by priority of index, and denote the results by {X _n(1),…, X _n(n). Thus

$$|X_{n}(1)|\geq |X_{n}(2)|\geq ...\geq |X_{n}(n)|$$

and X _n(j)= X _k if and only if #i ≤n: ∣X _i∣ > ∣X _k∣, or ∣X _i∣ = ∣X _k∣ and i ≤k= j.