Conference Agenda

In this talk, we consider a two-sample smooth test for testing the equality of multivariate distributions. Dependency between the two samples is allowed for. For instance, the data can be mixing. The asymptotic distribution under the null hypothesis is derived, and consistency of the two-sample smooth test for dependent samples is shown.

Satterthwaite (1941, 1946) proposed a very simple approximation to the distribution of linear combinations of Chi-squared random variables. It can be used in univariate time series analysis to approximate the distribution of the sample variance and the periodogram of Gaussian time series; we provide Wasserstein bounds and rates of convergence of the approximation towards the true distribution. Similarly, Tan & Gupta (1983) proposed an approximation to the distribution of linear combinations of Wishart random matrices. This, however, has not yet been applied to the framework of multivariate time series: we take advantage of a special case of the matrix normal distribution to propose a feasible approximation to the distribution of the sample covariance matrix of Gaussian time series.