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Eduardo Gutiérrez-Peña

Publications and source records attributed to Eduardo Gutiérrez-Peña.

5 recordsLinked to original sources
arXiv2025

Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem by shifting the stochastic dynamics to the associated subordinator, enabling a parametric estimation procedure without requiring additional assumptions. This reformulation allows for efficient numerical recovery of the likelihood function via Laplace transform inversion, even in models where closed-form transition densities are unavailable. In addition to offering a flexible approach to parameter estimation, we propose a dynamic simulation framework that generates discrete-time trajectories of CSBPs using the same subordinator-based structure.

stat.ME↗
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↗
arXiv2021

General dependence structures for some models based on exponential families with quadratic variance functions

We describe a procedure to introduce general dependence structures on a set of random variables. These include order-$q$ moving average-type structures, as well as seasonal, periodic, spatial and spatio-temporal dependences. The invariant marginal distribution can be in any family that is conjugate to an exponential family with quadratic variance function. Dependence is induced via a set of suitable latent variables whose conditional distribution mirrors the sampling distribution in a Bayesian conjugate analysis of such exponential families. We obtain strict stationarity as a special case.

math.ST↗
arXiv2019

A novel characterization and new simple tests of multivariate independence using copulas

The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of multivariate independence for continuous random vectors. The tests rely on estimating the checkerboard approximation by means of the sample copula recently introduced in [9] and improved in [11]. Such estimators have nice properties, including a Glivenko-Cantelli-type theorem that guarantees almost-sure uniform convergence to the checkerboard approximation. Each of our test statistics is defined in terms of one of a number of different metrics, including the supremum, total variation and Hellinger distances, as well as the Kullback-Leibler divergence. All of these tests can be easily implemented since the corresponding test statistics can be efficiently simulated under any alternative hypothesis, even for moderate and large sample sizes in relatively large dimensions. Finally, we assess the performance of our tests by means of a simulation study and provide one real data example.

math.ST↗