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The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
The extremal index $\theta$, a measure of the degree of local dependence in the extremes of a stationary process, plays an important role in extreme value analyses. We estimate $\theta$ semiparametrically, using the relationship between the…
We extend the constrained maximum likelihood estimation theory for parameters of a completely identified model, proposed by Aitchison and Silvey (1958), to parameters arising from a partially identified model. With a partially identified…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
One of the classic data mining tasks is to discover bursts, time intervals, where events occur at abnormally high rate. In this paper we revisit Kleinberg's seminal work, where bursts are discovered by using exponential distribution with a…
Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them…
This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case…
High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for…
A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…
Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modelling of extremes is therefore essential if the spatial…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…