We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate "B"-splines of lagged observations and volatilities. Estimation of such a "B"-spline...

As a powerful tool for analyzing full conditional (in-)dependencies between random variables, graphical models have become increasingly popular to infer genetic networks based on gene expression data. However, full (unconstrained) conditional relationships between random variables can be only...

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis, is notoriously difficult, especially for high dimensional data. We introduce stability selection. It is based on subsampling in combination with (high dimensional) selection algorithms. As such, the...

We study the properties of an MA([infinity])-representation of an autoregressive approximation for a stationary, real-valued process. In doing so we give an extension of Wiener's theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain...

We apply the blockwise bootstrap for stationary observations, proposed by Künsch (1989), to empirical processes indexed by function classes which satisfy some bracketing conditions. We prove a bootstrap central limit theorem for empirical processes of stationary [beta]-mixing variables, which...

Random Forests in combination with Stability Selection allow to estimate stable conditional independence graphs with an error control mechanism for false positive selection. This approach is applicable to graphs containing both continuous and discrete variables at the same time. Its performance...