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Second-order linearity of the general signed-rank statistic

Author

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  • Kersting, G.

Abstract

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 0 in probability, as n --> [infinity]. Vn is asymptotically normal.

Suggested Citation

  • Kersting, G., 1987. "Second-order linearity of the general signed-rank statistic," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 274-295, April.
    • Handle: RePEc:eee:jmvana:v:21:y:1987:i:2:p:274-295
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    Cited by:

    1. Marek Omelka, 2007. "Second-order Linearity of Wilcoxon Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 385-402, June.

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