arXiv subjects

Miguel Lafuente

Publications and source records attributed to Miguel Lafuente.

5 recordsLinked to original sources

arXiv2026

Estimating the tail index of Pareto-type distributions from geometric records

In this paper, we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish strong consistency and asymptotic normality, providing also an explicit expression for the asymptotic variance. These results are then extended to a broad class of Pareto-type distributions. The performance of the estimator is assessed via Monte Carlo simulation and compared with classical estimators from the literature. The proposed method is particularly well suited for settings where data arrive sequentially, as it yields smooth estimation trajectories. It is also especially advantageous in applications such as destructive testing, where measuring each item is costly. In this context, the estimator achieves a comparable level of estimation accuracy to Hill's estimator, but with a considerably lower number of fully measured items. An application to the analysis of the distribution of fluctuations of the Dow Jones Industrial Average (DJI) is also presented.

math.ST↗

arXiv2025

Characterisation of distributions via record-like observations

We characterise probability distributions via a martingale property associated with a natural generalisation of record values, known as $δ$-records. For an independent and identically distributed sequence $(X_n)$ with running maximum $M_n$, let $N_n$ be the number of $δ$-records (those $X_k$ with $X_k>M_{k-1}+δ$). We determine distributions for which $N_n-cM_n$ is a martingale, and show that this property uniquely determines the underlying distribution within broad classes. We show that the problem can be reformulated in terms of a delay-integrated Cauchy functional equation. A distinctive feature of this equation is that it is required to hold on a set that depends on the unknown distribution itself, which both complicates the analysis and allows for a rich variety of solutions. A complete characterisation is obtained when $δ<0$. For $δ>0$, all solutions with bounded support are identified. In the case of $δ>0$ and unbounded support, we consider both continuous and lattice distributions. In the continuous case, the characterisation reduces to a delay differential equation, which admits classical exponential-type solutions as well as broader families, including mixtures of exponential and gamma distributions. An analogous discrete analysis leads to difference equations whose solutions include mixtures of geometric and negative binomial distributions. In particular, this yields a new characterisation of the geometric distribution based on weak records.

math.PR↗

arXiv2025

Estimating hazard rates from $δ$-records in discrete distributions

This paper focuses on nonparametric statistical inference of the hazard rate function of discrete distributions based on $δ$-record data. We derive the explicit expression of the maximum likelihood estimator and determine its exact distribution, as well as some important characteristics such as its bias and mean squared error. We then discuss the construction of confidence intervals and goodness-of-fit tests. The performance of our proposals is evaluated using simulation methods. Applications to real data are given, as well. The estimation of the hazard rate function based on usual records has been studied in the literature, although many procedures require several samples of records. In contrast, our approach relies on a single sequence of $δ$-records, simplifying the experimental design and increasing the applicability of the methods.

math.ST↗

arXiv2022

Spatial modeling of day-within-year temperature time series: an examination of daily maximum temperatures in Aragón, Spain

Acknowledging a considerable literature on modeling daily temperature data, we propose a multi-level spatio-temporal model which introduces several innovations in order to explain the daily maximum temperature in the summer period over 60 years in a region containing Aragón, Spain. The model operates over continuous space but adopts two discrete temporal scales, year and day within year. It captures temporal dependence through autoregression on days within year and also on years. Spatial dependence is captured through spatial process modeling of intercepts, slope coefficients, variances, and autocorrelations. The model is expressed in a form which separates fixed effects from random effects and also separates space, years, and days for each type of effect. Motivated by exploratory data analysis, fixed effects to capture the influence of elevation, seasonality and a linear trend are employed. Pure errors are introduced for years, for locations within years, and for locations at days within years. The performance of the model is checked using a leave-one-out cross-validation. Applications of the model are presented including prediction of the daily temperature series at unobserved or partially observed sites and inference to investigate climate change comparison.

stat.ME↗

arXiv2020

Exact and asymptotic properties of $δ$-records in the linear drift model

The study of records in the Linear Drift Model (LDM) has attracted much attention recently due to applications in several fields. In the present paper we study $δ$-records in the LDM, defined as observations which are greater than all previous observations, plus a fixed real quantity $δ$. We give analytical properties of the probability of $δ$-records and study the correlation between $δ$-record events. We also analyse the asymptotic behaviour of the number of $δ$-records among the first $n$ observations and give conditions for convergence to the Gaussian distribution. As a consequence of our results, we solve a conjecture posed in J. Stat. Mech. 2010, P10013, regarding the total number of records in a LDM with negative drift. Examples of application to particular distributions, such as Gumbel or Pareto are also provided. We illustrate our results with a real data set of summer temperatures in Spain, where the LDM is consistent with the global-warming phenomenon.

math.ST↗