Multivariate Nonparametric Methods with R: An approach based on spatial signs and ranks

By Hannu Oja. 2010

202 citations recorded by the source corpus.

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Citations in the corpus

Robust multivariate nonparametric tests via projection averaging (2018, background): “Although there has been much effort to extend univariate sign- or rank-based statistics in a multivariate space (see e.g. Hettmansperger et al., 1998; Oja and Randles, 2004; Liu, 2006; Oja, 2010), they are either computationally expensive to implement or less intuitive to understand.”
Nonparametric multivariate rank tests and their unbiasedness (2012, background): “Other authors have constructed various permutation tests: Bickel [3], Brown [4], Hall and Tajvidi [14], Neuhaus and Zhu [26], Oja [28], Wellner [42] and others.”
A cautionary note on robust covariance plug-in methods (2014, methodology): “2 Joint independence and symmetrization Of the scatter functionals considered so far, only cov and wcov2 are known to be diagonal whenever the components are mutually independent. Oja et al. (2006) refer to this property as the independence property and discuss its importance in independent componen”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “…Rizzo, and Bakirov (2007), Berrett and Samworth (2019), Gretton, Fukumizu et al. (2008), Heller, Heller, and Gorfine (2013), Biswas, Sarkar, and Ghosh (2016), Gieser and Randles (1997), Taskinen, Oja, and Randles (2005), Oja (2010), and Friedman and Rafsky (1983) and the references therein.”
Nonlinear sufficient dimension reduction for functional data (2017, unknown): “See, for example, Oja (2010).”
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions (2013, background): “However, the following proposition, essentially coming fromMarden (1999) and Croux, Ollila, and Oja (2002) (also explicitly stated as Theorem 4.4 in Oja (2010)), states that the eigenspace of the multivariate Kendall’s tau statistic K is identical to the eigenspace of the covariance matrix .”
Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, background): “This class of multivariate ranks (Möttönen and Oja 1995; Möttönen et al. 1997; Chaudhuri 1996; Koltchinskii 1997; Oja and Randles 2004, Oja 2010, and many others) includes several very ingenious, elegant, and appealing concepts.”
Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem (2016, methodology): “In traditional fixed p circumstance, the following so-called “inner centering and inner standardization” sign-based procedure is usually used (Oja 2010, sec.”
Testing independence in high dimensions with sums of rank correlations (2015, methodology): “If X is normal, then under the traditional asymptotic setup in which n goes to ∞ while m is fixed, the likelihood ratio test (LRT) statistic converges to a chi-square distribution when H0 is true Anderson (2003). This test is known to be unimplementable for m > n due to the singularity of the sample”