- using R Under development (unstable) (2024-12-10 r87437)
- using platform: x86_64-pc-linux-gnu
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clang version 19.1.5
flang-new version 19.1.5
- running under: Fedora Linux 36 (Workstation Edition)
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- this is package ‘DepthProc’ version ‘2.1.5’
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See the install log for details.
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Specified C++11: please drop specification unless essential
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checkRd: (-1) asymmetryCurve.Rd:38: Lost braces; missing escapes or markup?
38 | For sample depth function \eqn{ D({x}, {{{Z}} ^ {n}}) }, \eqn{ {x} \in {{{R}} ^ {d}} }, \eqn{ d \ge 2 }, \eqn{ {Z} ^ {n} = \{{{{z}}_{1}}, ..., {{{z}}_{n}}\} \subset {{{R}} ^ {d}} }, \eqn{ {{D}_{\alpha}}({{{Z}} ^ {n}}) } denoting \eqn{ \alpha } --- central region, we can define {the asymmetry curve} \eqn{ AC(\alpha) = \left(\alpha, \left\| {{c} ^ {-1}}(\{{\bar{z}} - med|{{D}_{\alpha}}({{{Z}} ^ {n}})\}) \right\|\right) \subset {{{R}} ^ {2}} }, for \eqn{ \alpha \in [0, 1] } being nonparametric scale and asymmetry functional correspondingly, where \eqn{ c } --- denotes constant, \eqn{ {\bar{z}} } --- denotes mean vector, denotes multivariate median induced by depth function and \eqn{ vol } --- denotes a volume.
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checkRd: (-1) mWilcoxonTest.Rd:26: Lost braces; missing escapes or markup?
26 | Properties of the DD plot based statistics in the i.i.d setting were studied by Li & Liu (2004). Authors proposed several DD-plot based statistics and presented bootstrap arguments for their consistency and good effectiveness in comparison to Hotelling \eqn{ T ^ 2 } and multivariate analogues of Ansari-Bradley and Tukey-Siegel statistics. Asymptotic distributions of depth based multivariate Wilcoxon rank-sum test statistic under the null and general alternative hypotheses were obtained by Zuo & He (2006). Several properties of the depth based rang test involving its unbiasedness was critically discussed by Jureckova & Kalina (2012). Basing on DD-plot object, which is available within the \pkg{DepthProc} it is possible to define several multivariate generalizations of one-dimensional rank and order statistics in an easy way. These generalizations cover well known {Wilcoxon rang-sum statistic}.
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- DONE
Status: 2 NOTEs