Related papers: Adaptive Bernstein Copulas and Risk Management
To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…
In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields.…
Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and…
We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…
Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper,…
Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their…
Key to effective generic, or "black-box", variational inference is the selection of an approximation to the target density that balances accuracy and speed. Copula models are promising options, but calibration of the approximation can be…
By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), this paper proposes a framework to decouple marginal distributions from the dependence structure, clarifying interactions among binary variables. Explicit…
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to…
We propose a new methodology based on the Marshall-Olkin (MO) copula to model cross-border systemic risk. The proposed framework estimates the impact of the systematic and idiosyncratic components on systemic risk. Initially, we propose a…