Testing for Spherical Symmetry of a Multivariate Distribution

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...

Screening for a Multivariate Mixture Normal Distribution

HYPOTHESIS TESTING FOR AN EXCHANGEABLE NORMAL DISTRIBUTION

Consider an exchangeable normal vector with parameters ????2, and ?. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given.

screening for a multivariate mixture normal distribution

T3-Plot for Testing Spherical Symmetry for High-Dimensional Data with a Small Sample Size

High-dimensional data with a small sample size, such as microarray data and image data, are commonly encountered in some practical problems for which many variables have to be measured but it is too costly or time consuming to repeat the measurements for many times. Analysis of this kind of data poses a great challenge for statisticians. In this paper, we develop a new graphical method for test...