Asymptotic Properties of the Wilcoxon-Mann-Whitney Statistic
Asymptotic Properties of the Wilcoxon-Mann-Whitney Statistic
DOI:
https://doi.org/10.56143/ujmcs.v1i2.9Ключевые слова:
associated; statistics; stationary; sequence.Аннотация
Random variables seen in many practical problems of statistical physics, quantum field theory, and reliability theory are associated connected random variables. This article focuses on nonparametric estimates for statistics constructed by associated random variables. It proves a theorem for a sequence of stationary associated random variables with two identical marginal distributions.
Библиографические ссылки
[1] Bagai, I. and Prakasa Rao, B.L.S. Estimation of the survival function for stationary associated processes, Statist. Probab. Lett., 12, 385-391.(1991)
[2] Baek, Jong Li., Park, Sung Tae., Chung, Sung Mo. and Seo, Hye Young. On the almost sure convergence of weighted sums of negatively associated random variables, Commun. Korean Math. Soc., 20, 539-546. (2005).
[3] Bagai, I. and Prakasa Rao, B.L.S. Kernel-type density and failure rate estimation for associated sequences, Ann. Inst. Statist. Math., 47,
253-266.(1995)
[4] Birkel, T. On the convergence rate in the central limit theorem for associated processes, Ann. Probab., 16, 1689-1698.(1988b)
[5] Bulinski, A.V. Rates of convergence in the central limit theorem for fields of associated random variables, Theor. Probab. Appl., 40, 136-144.(1995)
[6] Matula, P. On almost sure limit theorems for positively dependent random variables, Statist. Probab. Lett., 74, 59-66.(2005)
[7] Newman, C.M. and Wright, A.L. Associated random variables and martingale inequalities, Z. Wahrsch. Theorie und Verw. Gebiete, 59, 361-371.(1982)
[8] Hoeffding, W. Masstabinvariante Korrelations-theorie, Schr. Math. Inst.University Berlin, 5, 181-233. (1940)
[9] Queseda- Molina, J.J. A generalization of an identity of Hoeffding and some applications, J. Ital. Statist. Soc., 3, 405-411.(1992)
