L1 Rates of Convergence for Linear Rank Statistics

This paper gives rates of convergence for the L1 distances between the distributions of standardized linear rank statistics and the standard normal random variable. These rates are O(N-1/2) under various conditions on the score function and the distributions of the underlying observations.

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Bibliographic Details
Published in:The Annals of statistics 1976-07, Vol.4 (4), p.771-774
Main Authors: Erickson, R. V., Koul, H. L.
Format: Article
Language:English
Subjects:
Mathematical constants
Mathematical theorems
Null hypothesis
Random variables
Short Communications
Statistical theories
Statistics
Online Access:Get full text
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Description
Summary:This paper gives rates of convergence for the L1 distances between the distributions of standardized linear rank statistics and the standard normal random variable. These rates are O(N-1/2) under various conditions on the score function and the distributions of the underlying observations.
ISSN:0090-5364
DOI:10.1214/aos/1176343549