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On a Class of Nonparametric Tests for Independence—Bivariate Case(1)

Published online by Cambridge University Press:  20 November 2018

M. S. Srivastava
M. S. Srivastava*
Affiliation:
University of Toronto, Toronto, Ontario
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Let(X1, Y1), (X2, Y2),…, (Xn, Yn) be n mutually independent pairs of random variables with absolutely continuous (hereafter, a.c.) pdf given by

(1)

where f(ρ) denotes the conditional pdf of X given Y, g(y) the marginal pdf of Y, e(ρ)→ 1 and b(ρ)→0 as ρ→0 and,

(2)

We wish to test the hypothesis

(3)

against the alternative

(4)

For the two-sided alternative we take — ∞< b < ∞. A feature of the model (1) is that it covers both-sided alternatives which have not been considered in the literature so far.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 337 - 342
Copyright
Copyright © Canadian Mathematical Society 1973

Footnotes

(1)

Research supported partially by Canada Council and National Research Council of Canada.

References

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