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- W2014955138 abstract "The rank statistic $$S_n({bf t}) = 1 / n sum^{n}_{i=1} c_i R_{i}({bf t}) ({bf t} in mathbb{R}^{p})$$ , with R i (t) being the rank of $$e_{i}-{bf t}^{hbox{T}}{bf x}_i, i=1,ldots,n$$ and e 1 , . . . , e n being the random sample from a distribution with a cdf F, is considered as a random process with t in the role of parameter. Under some assumptions on c i , x i and on the underlying distribution, it is proved that the process $${S_n(frac{{bf t}}{sqrt{n}})-S_n(mathbf{0}) - {rm E} S_{n}({bf t}), |{bf t}|_2 leq M}$$ converges weakly to the Gaussian process. This generalizes the existing results where the one-dimensional case $${bf t} in mathbb{R}$$ was considered. We believe our method of the proof can be easily modified for the signed-rank statistics of Wilcoxon type. Finally, we use our results to find the second order asymptotic distribution of the R-estimator based on the Wilcoxon scores and also to investigate the length of the confidence interval for a single parameter β l ." @default.
- W2014955138 created "2016-06-24" @default.
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- W2014955138 date "2006-06-28" @default.
- W2014955138 modified "2023-09-25" @default.
- W2014955138 title "Second-order Linearity of Wilcoxon Statistics" @default.
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- W2014955138 doi "https://doi.org/10.1007/s10463-006-0054-8" @default.
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