Pedro C. Alvarez-Esteban

• PhD
• University of Valladolid

Predictable operations are the basis of efficient air traffic management. In this context, accurately estimating the arrival time to the destination airport is fundamental to make tactical decisions about an optimal schedule of landing and take-off operations. In this paper, we evaluate different deep learning models based on LSTM architectures for...

A robust approach for clustering functional directional data is proposed. The proposal adapts “impartial trimming” techniques to this particular framework. Impartial trimming uses the dataset itself to tell us which appears to be the most outlying curves. A feasible algorithm is proposed for its practical implementation justified by some theoretica...

This paper analyses COVID-19 patients’ dynamics during the first wave in the region of Castilla y León (Spain) with around 2.4 million inhabitants using multi-state competing risk survival models. From the date registered as the start of the clinical process, it is assumed that a patient can progress through three intermediate states until reaching...

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new treatment significantly better than the old?'. However, this is only partially answered by some of the usual sta...

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new treatment significantly better than the old?'. However, this is only partially answered by some of the usual sta...

Stochastic ordering among distributions has been considered in a variety of scenarios. However, it is often a restrictive model, not supported by the data even in cases in which the researcher tends to believe that a certain variable is somehow smaller than other. Alternatively, we propose to look at a more flexible version in which two distributio...

Let P2,ac be the set of Borel probabilities on Rd with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fréchet mean) of a finite set of probabilities ν1,...,νk∈P2,ac with respect to the L2-Wasserstein metric. For this task we introduce an operator on P2,ac relate...

We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we consider a ``wide consensus" procedure. The approach is based on the consideration of trimmed barycenters in the W...

Let $\mathcal{P}_{2,ac}$ be the set of Borel probabilities on $\mathbb{R}^d$ with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fr\'echet mean) of a finite set of probabilities $\nu_1,\ldots,\nu_k \in \mathcal{P}_{2,ac}$ with respect to the $L_2-$Wasserstein me...

A time series clustering algorithm based on the use of the total variation distance between normalized spectra as a measure of dissimilarity is proposed in this work. The oscillatory behavior of the series is thus considered the central characteristic for classification purposes. The proposed algorithm is compared to several other methods which are...

Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic orderings are often a too strong assumption which is not supported by the data even in cases in which the resear...

The problem of detecting changes in the state of the sea is very important for the analysis and determination of wave climate in a given location. Wave measurements are frequently statistically analyzed as a time series, and segmentation algorithms developed in this context are used to determine change-points. However, most methods found in the lit...

The grades of a Spanish university access exam involving 10 graders are analyzed. The interest focuses on finding the greatest group of graders showing similar grading patterns or, equivalently, on detecting if there are graders whose grades exhibit significant deviations from the pattern determined by the remaining graders. Due to differences in b...

Random sea waves are often modeled as stationary processes for short or moderately long periods of time and therefore the problem of detecting changes in the sea state is very important. We look at this problem from the spectral point of view, proposing a method based on the total variation distance. The method considers processes normalized to hav...

We say that two probabilities are similar at level $\alpha$ if they are contaminated versions (up to an $\alpha$ fraction) of the same common probability. We show how this model is related to minimal distances between sets of trimmed probabilities. Empirical versions turn out to present an overfitting effect in the sense that trimming beyond the si...

: In this work we look at the spectral evolution of waves from the point of view of the total variation (TV) distance. There are several methods for determining changes in the variance of a random process, which correspond to changes in the total energy of the waves. We look instead at changes in the distribution of the energy as given by the energ...

For α∈(0, 1) an α-trimming, P∗, of a probability P is a new probability obtained by re-weighting the probability of any Borel set, B, according to a positive weight function, f≤1/(1−α), in the way P∗(B)=∫Bf(x)P(dx). ¶ If P, Q are probability measures on Euclidean space, we consider the problem of obtaining the best L2-Wasserstein approximation betw...

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. The L2-Wasserstein distance is used to introduce the trimming methodology for assessing wh...

En esta tesis se desarrolla una metodología de recortes imparciales (dirigidos por los datos) en el ámbito de la comparación de distribuciones y los test de ajuste, y se obtienen algoritmos y resultados que permiten su aplicación en el análisis de datos y en la inferencia estadística. Los procedimientos que se desarrollan permiten el estudio de la...

In this paper, we introduce logistic models to analyse fertility curves. The models are formulated as linear models of the log odds of fertility and are defined in terms of parameters that are interpreted as measures of level, location and shape of the fertility schedule. This parameterization is useful for the evaluation, and interpretation of fer...

This article introduces an analysis of similarity of distributions based on the L2-Wasserstein distance between trimmed distributions. Our main innovation is the use of the impartial trimming methodology, already considered in robust statistics, which we adapt to this setup. Instead of simply removing data at the tails to provide some robustness to...

Statistical methods of dimension reduction and classification are used to obtain homogeneous local-area clustering with regard to the most relevant demographic parameters. The dimension reduction is conducted in two stages using Principal Component Analysis and a modified k-mean procedure is proposed to determine the final clusters. This clustering...

Impartial trimming methods as developed in (1) and (2) can be con- sidered not only as a way to robustify statistical procedures but also as a method to discard a part of the data to achieve the best possible t between a sample and a theoretical distribution or between two given samples. This point of view is adopted in this work with respect to th...