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Rank Tests for Bivariate Symmetry
- Source :
- Annals of statistics, 9(5), 1087-1095, Ann. Statist. 9, no. 5 (1981), 1087-1095
- Publication Year :
- 1981
-
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.
- Subjects :
- Statistics and Probability
Nonparametric tests
62C99
62E20
Reduction (recursion theory)
Rank (linear algebra)
media_common.quotation_subject
asymptotic normality
Mathematical analysis
Asymptotic distribution
Invariant (physics)
locally most powerful tests
Asymmetry
bivariate symmetry and asymmetry
Combinatorics
Joint probability distribution
Statistics, Probability and Uncertainty
Symmetry (geometry)
Bijection, injection and surjection
media_common
Mathematics
62G10
62A05
Subjects
Details
- Language :
- English
- ISSN :
- 00905364
- Database :
- OpenAIRE
- Journal :
- Annals of statistics, 9(5), 1087-1095, Ann. Statist. 9, no. 5 (1981), 1087-1095
- Accession number :
- edsair.doi.dedup.....f10f5d76b5bd7a910b0c80846bad52f3