Second-order linearity of the general signed-rank statistic

Let X1,..., Xn be i.i.d. random variables symmetric about zero. Let Ri(t) be the rank of Xi - tn-1/2 among X1 - tn-1/2,..., Xn - tn-1/2 and Tn(t) = [Sigma]i = 1n[phi]((n + 1)-1Ri(t))sign(Xi - tn-1/2). We show that there exists a sequence of random variables Vn such that sup0 <= t <= 1 Tn(t) - Tn(0) - tVn --> 0 in probability, as n --> [infinity]. Vn is asymptotically normal.

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Year of publication:	1987
Authors:	Kersting, G.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 21.1987, 2, p. 274-295
Publisher:	Elsevier
Keywords:	Signed-rank statistic weak convergence symmetric distributions

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005221268