Open Access
September, 1981 Rank Tests for Bivariate Symmetry
Tom Snijders
Ann. Statist. 9(5): 1087-1095 (September, 1981). DOI: 10.1214/aos/1176345588

Abstract

The problem is considered of testing symmetry of a bivariate distribution $\mathscr{L}(X, Y)$ against "asymmetry towards high $X$-values," subject to the restriction of invariance under the transformations $(x_i, y_i) \mapsto (g(x_i), g(y_i)) (1 \leq i \leq n)$ for increasing bijections $g$. This invariance restriction prohibits the common reduction to the differences $x_i - y_i$. The intuitive concept of "asymmetry towards high $X$-values" is approached in several ways, and a mathematical formulation for this concept is proposed. Most powerful and locally most powerful invariant similar tests against certain subalternatives are characterized by means of a Hoeffding formula. Asymptotic normality and consistency results are obtained for appropriate linear rank tests.

Citation

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Tom Snijders. "Rank Tests for Bivariate Symmetry." Ann. Statist. 9 (5) 1087 - 1095, September, 1981. https://doi.org/10.1214/aos/1176345588

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0478.62031
MathSciNet: MR628764
Digital Object Identifier: 10.1214/aos/1176345588

Subjects:
Primary: 62G10
Secondary: 62A05 , 62C99 , 62E20

Keywords: asymptotic normality , bivariate symmetry and asymmetry , locally most powerful tests , nonparametric tests

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 5 • September, 1981
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