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Sign test of independence between two random vectors

✍ Scribed by Sara Taskinen; Annaliisa Kankainen; Hannu Oja

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
165 KB
Volume
62
Category
Article
ISSN
0167-7152

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✦ Synopsis

A new a ne invariant extension of the quadrant test statistic Blomqvist (Ann. Math. Statist. 21 (1950) 593) based on spatial signs is proposed for testing the hypothesis of independence. In the elliptic case, the new test statistic is asymptotically equivalent to the interdirection test by Gieser and Randles (J. Amer. Statist. Assoc. 92 (1997) 561) but is easier to compute in practice. Limiting Pitman e ciencies and simulations are used to compare the test to the classical Wilks' test.

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## I. fntFoduction Let {X,,, n 2 1) be a sequence of independent random variables, P, and f, the distribution function and the characteristic fundion of the X,, respectively. Let us put SN = 2 X,, where N is a pasitive integer-valued random variable independent of X,, ?t 2 1. Furthermore, let { P,