Related papers: Applications of the Quantile-Based Probabilistic M…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when the risks are randomly right-censored.…
In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We propose a novel conditional diffusion model for contextual portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on high-dimensional asset-specific factors. Our model leverages a…
Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for…
The concept of trustworthy AI has gained widespread attention lately. One of the aspects relevant to trustworthy AI is robustness of ML models. In this study, we show how to probabilistically quantify robustness against naturally occurring…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…