Robust multivariate nonparametric tests via projection averaging

By Ilmun Kim, Sivaraman Balakrishnan, Larry A. Wasserman. Annals of Statistics, 2018

75 citations recorded by the source corpus.

In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed data and minimax rate optimal against a certain class of alternatives. Our test statistic is completely free of tuning parameters and is computationally efficient even in high dimensions. When the dimension tends to infinity, the proposed test is shown to have comparable power to the existing high-dimensional mean tests under certain location models. As a by-product of our approach, we introduce a new metric called the angular distance which can be thought of as a robust alternative to the Euclidean distance. Using the angular distance, we connect the proposed method to the reproducing kernel Hilbert space approach. In addition to the Cram\'er-von Mises statistic, we demonstrate that the projection-averaging technique can be used to define robust, multivariate tests in many other problems.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b4f7a8333a7f8766a8aa28ca73044b4e12cf6f19

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

  1. Fang Han
  2. Hongjian Shi
  3. Mathias Drton
  4. Marloes H. Maathuis
  5. Sacha Epskamp
  6. Bodhisattva Sen
  7. Nabarun Deb
  8. Zhexiao Lin

Citations in the corpus