Day 1 (Tuesday 2 April) @ 13:45–15:15

Eni Musta (University of Amsterdam)

Single-index mixture cure model under monotonicity constraints

We consider survival data with a cure fraction, meaning that some subjects never experience the event of interest. For example, in oncology the event of interest is cancer relapse/death and the cured patients after treatment are immune to such event. It is common in this context to use a mixture cure model, consisting of two sub-models: one for the probability of being uncured (incidence) and one for the survival of the uncured subjects (latency). Various approaches, ranging from parametric to nonparametric, have been proposed to model the incidence component, with the logistic model being the standard choice. We consider a monotone single-index model for the incidence, which relaxes the parametric logistic assumption, while maintaining interpretability of the regression coefficients and avoiding the curse-of-dimensionality. A new estimation method is introduced that relies on the profile maximum likelihood principle, techniques from isotonic regression and kernel smoothing. We discuss some unique and challenging issues that arise when incorporating the monotone single-index model within the mixture cure model. The consistency of the proposed estimator is established and its practical performance is investigated through a simulation study and an application to melanoma cancer data.

Joint work with Tsz Pang Yuen.

Fabian Mies (TU Delft)

 Likelihood asymptotics for stationary Gaussian arrays

Arrays of stationary Gaussian time series can arise naturally in econometric applications, e.g. as the discretization of continuous-time stochastic processes, or be introduced artificially to model persistency via so-called local-to-unity models, i.e. linear time series models with parameters close to a unit root. For the parametric statistical estimation of these stationary models, the spectral density plays a central role. In particular, classical results in time series analysis suggest that the Gaussian likelihood and Fisher information may be approximated in terms of the spectral density, and conditions for efficiency of the MLE have been formulated in the literature. Unfortunately, these general results do not cover arrays of time series. Our contribution is to show in which way the asymptotic likelihood theory needs to be adapted for the array case, and we demonstrate that this yields a straight-forward approach to study a broad class of processes.

As a motivating example, we investigate the estimation of the mixed fractional Brownian motion based on high-frequency observations. Our findings reveal that the achievable rates of convergence depend intricately on the size of the various components, as well as their intertemporal and crosstemporal dependence structure.

Frank Röttger (Eindhoven University of Technology)

Structural causal models in multivariate extremes from threshold exceedances

Structural causal models (SCMs) are a fundamental tool in causal inference that allow for flexible dependence modeling. In this talk we discuss a new approach to model the extremal behavior of SCMs. We introduce a limiting extremal SCM that conforms with extremal Markov properties based on the recently introduced notion of extremal conditional independence. This yields a definition of directed graphical models for multivariate extremes from threshold exceedances.

For the parametric subclass of Hüsler–Reiss distributions, which are considered as an analogue of Gaussian distributions in extremes, we find simple a linear extremal SCM that permits a parametric description of extremal conditional independence. 

This gives rise to a simple extremal conditional independence test, which we implement in a PC-type algorithm and demonstrate on real data.

This is joint work with Sebastian Engelke and Nicola Gnecco.