Related papers: Low probability states, data statistics, and entro…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
The theory of Extreme Physical Information (EPI) is used to deduce a probability density function (PDF) of a system that exhibits a power law tail. The computed PDF is useful to study and fit several observed distributions in complex…
So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average…
We theoretically derive the probability densities of the entanglement measures of a pure non-ergodic many-body state, represented in a bipartite product basis and with its reduced density matrix described by a generalized, multi-parametric…
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…
We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…
We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
Gaussian and Laplacian entropy models are proved effective in learned point cloud attribute compression, as they assist in arithmetic coding of latents. However, we demonstrate through experiments that there is still unutilized information…
Subclassification estimators are one of the methods used to estimate causal effects of interest using the propensity score. This method is more stable compared to other weighting methods, such as inverse probability weighting estimators, in…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
Efficient and accurate state estimation is essential for the optimal management of the future smart grid. However, to meet the requirements of deploying the future grid at a large scale, the state estimation algorithm must be able to…
For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…