Abstract: (Goodness-of-Fit Tests for Censored and Truncated Data: A Gaussian Process Approach.)
In this talk I will present a new general strategy for goodness-of-fit testing with survival data. The setting is that of testing for a parametric family of distribution functions when the data are deteriorated due to random censoring and/or random truncation. A key step is the characterization of the null hypothesis through a moment equation which involves the estimation of the observable distribution under both the null and the alternative. An omnibus test based on a maximum mean discrepancy principle will be proposed, and its theoretical properties will be presented. The theoretical framework will be that of Gaussian processes and reproducing kernel Hilbert spaces. The finite sample performance of the proposed test will be investigated through simulations. Illustrative real data applications will be given. This is joint work with Juan Carlos Escanciano (Universidad Carlos III de Madrid)..

Abstract: (Copula-based measures for dependence between random vectors.)
The interest in this talk is in statistical (in)dependence between random vectors. Statistical independence between random vectors holds if and only if the true underlying copula is the product of the marginal copulas yielding zero dependence. We discuss some recent approaches towards developing dependence measures that completely characterize independence, such as phi-divergence measures, and optimal transport measures. We discuss statistical inference properties and provide illustrative examples. In high-dimensional settings possible marginal independencies can be taken into account by inducing (block) sparsity. This talk is based on joint work with Steven De Keyser