Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II

Václav Dupač, Jaroslav Hájek

Type: Article

Publication Date: 1969-12-01

Citations: 248

DOI: https://doi.org/10.1214/aoms/1177697281

Abstract

This is a straightforward continuation of Hajek (1968). We provide a further extension of the Chernoff-Savage (1958) limit theorem. The requirements concerning the scores-generating function are relaxed to a minimum: we assume that this function is a difference of two non-decreasing and square integrable functions. Thus, in contradistinction to Hajek (1968), we dropped the assumption of absolute continuity. The main results are accumulated in Section 2 without proofs. The proofs are given in Sections 4 through 7. Section 3 contains auxiliary results.

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The Annals of Mathematical Statistics - View - PDF

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