Related papers: Applications of the Quantile-Based Probabilistic M…
We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that,…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
We extend the univariate quantile based reliability concepts to the bivariate case using quantile curves. We propose quantile curves based bivariate hazard rate and bivariate mean residual life function and establish a relationship between…
The manuscript discusses how to incorporate random effects for quantile regression models for clustered data with focus on settings with many but small clusters. The paper has three contributions: (i) documenting that existing methods may…
The proportional hazards model represents the most commonly assumed hazard structure when analysing time to event data using regression models. We study a general hazard structure which contains, as particular cases, proportional hazards,…
In this paper, the author presents the generalized form of the Median-Based Unit Rayleigh (MBUR) distribution, a novel statistical distribution that is specifically defined within the interval (0, 1) expressing oscillating hazard rate…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…