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The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains foundational in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its…
Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution…
Multimodal regression is a fundamental task, which integrates the information from different sources to improve the performance of follow-up applications. However, existing methods mainly focus on improving the performance and often ignore…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
A new distribution on (0, 1), generalized Log-Lindley distribution, is proposed by extending the Log-Lindley distribution. This new distribution is shown to be a weighted Log-Lindley distribution. Important probabilistic and statistical…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…
We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations.…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…
We study 17 different statistical distributions for sizes obtained {}from the classical and recent literature to describe a relevant variable in the social sciences and Economics, namely the firms' sales distribution in six countries over…
Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate…
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…
This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be…
Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…