Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation

Nonparametric multivariate rank tests and their unbiasedness

JANA JUREČKOVÁ1 and JAN KALINA2 1Department of Probability and Statistics, Charles University in Prague, Sokolovská 83, CZ-186 75 Prague 8, Czech Republic. E-mail: [email protected] 2EUROMISE Center, Department of Medical Informatics, Institute of Computer Science of the Academy of Sciences of CR, v.v.i., Pod Vodárenskou věží 2, CZ-182 07 Prague 8, Czech Republic. E-mail: kalina@euromi...

Nonparametric multivariate conditional distribution and quantile regression

In nonparametric multivariate regression analysis, one usually seeks methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. We study nonparametric estimation of multivariate conditional distribution and quantile regression via local univariate quadratic estimation of partial derivatives of bivariate copulas. Without restri...

Multivariate nonparametric regression using lifting

For regularly spaced one-dimensional data wavelet shrinkage has proven to be a compelling method for nonparametric function estimation. We argue that this is not the case for irregularly spaced data in two or higher dimensions. This article develops three methods for the multiscale analysis of irregularly spaced data based on the recently developed lifting paradigm by “lifting one coefficient a...

Mann - Withney multivariate nonparametric control chart.

In many quality control applications, the necessary distributional assumptions to correctly apply the traditional parametric control charts are either not met or there is simply not enough information or evidence to verify the assumptions. It is well known that performance of many parametric control charts can be seriously degraded in situations like this. Thus, control charts that do not requi...

A Distribution-Free Theory of Nonparametric Regression