Testing Multivariate Symmetry

Testing Group Symmetry of a Multivariate Distribution

We propose and study a general class of tests for group symmetry of a multivariate distribution, which encompasses different types of symmetry, such as ellipsoidal and permutation symmetries among others. Our approach is based on supremum norms of special empirical processes combined with bootstrap. We show that these tests are consistent against any fixed alternative. This work generalizes the...

Multivariate Symmetry and Asymme- Try

Univariate symmetry has interesting and diverse forms of generalization to the multivariate case. Here several leading concepts of multivariate symmetry — spherical, elliptical, central and angular — are examined and various closely related notions discussed. Methods for testing the hypothesis of symmetry, and approaches for measuring the direction and magnitude of skewness, are reviewed.

Adaptive Multivariate Global Testing

We present a methodology for dealing with recent challenges in testing global hypotheses using multivariate observations. The proposed tests target situations, often arising in emerging applications of neuroimaging, where the sample size n is relatively small compared with the observations' dimension K. We employ adaptive designs allowing for sequential modifications of the test statistics adap...

Multivariate Extension of Put-Call Symmetry

Testing for Multivariate Volatility Functions

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i)...