arXiv subjects

Arturo Erdely

Publications and source records attributed to Arturo Erdely.

13 recordsLinked to original sources

arXiv2026

A subcopula characterization of dependence for the Multivariate Bernoulli Distribution

By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), this paper proposes a framework to decouple marginal distributions from the dependence structure, clarifying interactions among binary variables. Explicit formulas are derived under the MBD using subcopulas to introduce dependence measures for interactions of all orders, not just pairwise. A Bayesian inference approach is also applied to estimate the parameters of the MBD, offering practical tools for parameter estimation and dependence analysis in real-world applications. The results obtained contribute to the application of subcopulas of multivariate binary data, with real data examples.

stat.ME↗

arXiv2025

Visual analysis of bivariate dependence between continuous random variables

Scatter plots are widely recognized as fundamental tools for illustrating the relationship between two numerical variables. Despite this, based on solid theoretical foundations, scatter plots generated from pairs of continuous random variables may not serve as reliable tools for assessing dependence. Sklar's Theorem implies that scatter plots created from ranked data are preferable for such analysis as they exclusively convey information pertinent to dependence. This is in stark contrast to conventional scatter plots, which also encapsulate information about the variables' marginal distributions. Such additional information is extraneous to dependence analysis and can obscure the visual interpretation of the variables' relationship. In this article, we delve into the theoretical underpinnings of these ranked data scatter plots, hereafter referred to as rank plots. We offer insights into interpreting the information they reveal and examine their connections with various association measures, including Pearson's and Spearman's correlation coefficients, as well as Schweizer-Wolff's measure of dependence. Furthermore, we introduce a novel graphical combination for dependence analysis, termed a dplot, and demonstrate its efficacy through real data examples.

stat.ME↗

arXiv2023

A polynomial regression model for excess mortality in Mexico 2020-2022 due to the COVID-19 pandemic

Based on the comprehensive national death registry of Mexico spanning from 1998 to 2022 a point and interval estimation method for the excess mortality in Mexico during the years 2020-2022 is proposed based on illness-induced deaths only, using a polynomial regression model. The results obtained estimate that the excess mortality is around 788,000 people (39.3%) equivalently to a rate of 626 per 100,000 inhabitants. The male/female ratio is estimated to be 1.7 times. As a reference for comparison, for the whole period 2020-2020 Mexico's INEGI estimated an excess of mortality between 673,000 with a quasi-Poisson model and 808,000 using endemic channels estimation.

stat.AP↗

arXiv2023

Monografía de Estadística Bayesiana

Course notes about an introduction to Bayesian Statistics. First, an explanation of the bayesian paradigm is motivated and explained in detail (first three chapters). Then, a brief introduction to the basics about Decision Theory in chapter four, which is self contained, with the purpose of introducing parametrica bayesian inference as a decision problem in chapter five.

stat.OT↗

arXiv2022

Copula-based statistical dependence visualizations

A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The former is primarily limited because it reports a single value for a pair of random variables. Furthermore, scatter plots can fail to convey the dependency structure between variables properly. In this paper we discuss these shortcomings and present alternative and richer visualizations based on copula functions, which fully determine the dependency between continuous random variables. Since copulas seldom appear in the data visualization literature we first review essential theory, and propose alternative scatter plots and several heatmaps for assessing the statistical association between two continuous random variables. These visualizations not only allow users to detect independence, but also increasing and/or decreasing trends in the data through a color coding, which can also be applied in other methods such as parallel coordinates.

stat.AP↗

arXiv2019

Análisis estadístico ex post del conteo rápido institucional de la elección de gobernador del Estado de México en 2017

A statistical analysis of an electoral quick count based on the total count of votes in the election of the State of Mexico's governor in 2017 is performed in order to verify precision, confidence level of interval estimations, possible bias and derived conclusions therein, with the main purpose of checking compliance with the objectives of such statistical procedure. ----- Se realiza un análisis estadístico de las estimaciones del conteo rápido institucional desde la perspectiva ideal de los resultados de los cómputos distritales de la elección de gobernador del Estado de México del año 2017, particularmente aspectos como la precisión de las estimaciones, el nivel de confianza de los intervalos, el posible sesgo respecto al cómputo distrital y las conclusiones que se derivaron y reportaron, con el objetivo de determinar el grado de cumplimiento de los objetivos de este ejercicio estadístico de carácter informativo.

stat.AP↗

arXiv2019

A copula based approach for electoral quick counts

An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result before the total count of votes. A stratified sampling design is commonly preferred to reduce estimation variability. The present work shows that dependence among strata and among candidates should be taken into consideration for statistical inferences therein, and a copula based model is proposed and applied to Mexico's 2006, 2012, and 2018 presidential elections data.

stat.AP↗

arXiv2018

La falacia del empate técnico electoral

It is argued that the concept of "technical tie" in electoral polls and quick counts has no probabilistic basis, and that instead the uncertainty associated with these statistical exercises should be expressed in terms of a probability of victory of the leading candidate. ----- Se argumenta que el concepto de "empate técnico" en encuestas y conteos rápidos electorales no tiene fundamento probabilístico, y que en su lugar la incertidumbre asociada a dichos ejercicios estadísticos debiera expresarse en términos de una probabilidad de triunfo del candidato puntero.

stat.AP↗

arXiv2017

Copula-based piecewise regression

Most common parametric families of copulas are totally ordered, and in many cases they are also positively or negatively regression dependent and therefore they lead to monotone regression functions, which makes them not suitable for dependence relationships that imply or suggest a non-monotone regression function. A gluing copula approach is proposed to decompose the underlying copula into totally ordered copulas that combined may lead to a non-monotone regression function.

stat.ME↗

arXiv2017

A subcopula based dependence measure

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.

math.ST↗

arXiv2016

Value at risk and the diversification dogma

The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de diversificación de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de características individuales de los riesgos involucrados, así como de la relación de dependencia entre los mismos.

q-fin.RM↗

arXiv2016

A note on linear B-spline copulas

In this brief note we prove that linear B-spline copulas is not a new family of copulas since they are equivalent to checkerboard copulas, and discuss in particular how they are used to extend empirical subcopulas to copulas.

math.ST↗

arXiv2015

Backtesting forecast accuracy

A statistical test based on the geometric mean is proposed to determine if a predictive model should be rejected or not, when the quantity of interest is a strictly positive continuous random variable. A simulation study is performed to compare test power performance against an alternative procedure, and an application to insurance claims reserving is illustrated.

stat.ME↗