The Annals of Statistics

$L_1$ Rates of Convergence for Linear Rank Statistics

R. V. Erickson and H. L. Koul

Full-text: Open access

Abstract

This paper gives rates of convergence for the $L_1$ distances between the distributions of standardized linear rank statistics and the standard normal random variable. These rates are $O(N^{-\frac{1}{2}})$ under various conditions on the score function and the distributions of the underlying observations.

Article information

Source
Ann. Statist., Volume 4, Number 4 (1976), 771-774.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343549

Digital Object Identifier
doi:10.1214/aos/1176343549

Mathematical Reviews number (MathSciNet)
MR413356

Zentralblatt MATH identifier
0332.62010

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G99: None of the above, but in this section

Keywords
Linear rank statistics $L_1$ rates for asymptotic normality

Citation

Erickson, R. V.; Koul, H. L. $L_1$ Rates of Convergence for Linear Rank Statistics. Ann. Statist. 4 (1976), no. 4, 771--774. doi:10.1214/aos/1176343549. https://projecteuclid.org/euclid.aos/1176343549


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