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**Skills and Expertise**

## Publications

Publications (28)

Sensory analysis entails subjective valuations provided by qualified experts which in most of the cases are given by means of a real value. However personal valuations usually present an uncertainty in their meaning which is difficult to capture by using a unique value. In this work some statistical techniques to deal with such kind of information...

The convenient theoretical properties of the support function and the Minkowski addition-based arithmetic have been shown to be useful when dealing with compact and convex sets on Rp. However, both concepts present several drawbacks in certain contexts. The use of the radial function instead of the support function is suggested as an alternative to...

The space of nonempty convex and compact (fuzzy) subsets of Rp, Kc(Rp), has been traditionally used to handle imprecise data. Its elements can be characterized via the support function, which agrees with the usual Minkowski addition, and naturally embeds Kc(Rp) into a cone of a separable Hilbert space. The support function embedding holds interesti...

Classical
tests for the equality
of distributions of real-valued random variables are widely applied in Statistics. When the normality assumption for the variables fails, non-parametric techniques are to be considered; Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman tests, among other alternatives. Fuzzy representations of real-valued random varia...

The similarity degree
between the expectation
of two random intervals is studied by means of a hypothesis testing procedure. For this purpose, a similarity measure for intervals is introduced based on the so-called Jaccard index for convex sets. The measure ranges from 0 (if both intervals are not similar at all, i.e., if they are not overlapped) t...

Spanish primary and secondary school curricula comprise several contents, learning outcomes and assessment criteria directly related with probability and approximate calculus. Some of them refer to situations modeled by the students, which entail not only uncertainty but also imprecision. For this reason, different techniques including fuzzy logic...

Statistical methods for dealing with interval data have been developed for some time. Real intervals are the natural extension of real point values. They are commonly considered to generalize the nature of the experimental outcomes from the classical scenario to a more imprecise situation. Interval data have been mainly treated in the context of fu...

An ANOVA problem for interval-valued experimental data is considered. When a random variable is observed on several populations, the ANOVA technique focuses on testing whether the variable behaves significantly different on those groups. The theoretical formalization of the three-way ANOVA problem when the random element takes on interval values is...

We study the performance of recently developed linear regression models for interval data when it comes to forecasting the uncertainty surrounding future stock returns. These interval data models use easy-to-compute daily return intervals during the modeling, estimation and forecasting stage. They have to stand up to comparable point-data models of...

Real-life data associated with experimental outcomes are not always real-valued. In particular, opinions, perceptions, ratings, etc. are often assumed to be imprecise in nature, especially when they come from human valuations. Fuzzy numbers have long been considered to provide us with a convenient scale to express these imprecise data. In analyzing...

This note is a rejoinder on our paper in this issue. It attempts to provide some clarifications and thoughts in connection with the discussions/comments made about it by Didier Dubois and Sebastien Destercke. We hope our comments are at the level of the discussants'.

Inferential studies for the regression coefficients of a linear model for interval-valued random variables are addressed. Confidence sets and hypothesis tests are investigated and solved through asymptotic and bootstrap techniques. The inferences are based on the least-squares estimators of the model which have been shown to be coherent with the in...

The so-called fuzzy representations of real-valued random variables are reviewed. They are used to visualize or/and characterize distributions through fuzzy sets. Various fuzzy representations useful to explore or test about different characteristics of real distributions are described. The main developments concerning the representation, goodness-...

A new linear regression model for an interval-valued response and a real-valued explanatory variable is presented. The approach is based on the interval arithmetic. Comparisons with previous methods are discussed. The new linear model is theoretically analyzed and the regression parameters are estimated. Some properties of the regression estimators...

Data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified. Often the underlying imprecision can be suitably described in terms of fuzzy numbers/ values. For these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that...

Most of the research developed in the last years by the SMIRE Research Group concerns the statistical analysis of imprecisely (set- and fuzzy set)-valued experimental data. This analysis has been based on an approach considering the usual arithmetic for these data as well as suitable metrics between them. The research perfectly fits into the resear...

When working with real-valued data regression analysis allows to model and forecast the values of a random variable in terms of the values of either another one or several other random variables defined on the same probability space. When data are not real-valued, regression techniques should be extended and adapted to model simply relationships in...

Several linear regression models involving interval-valued variables have been formalized based on the interval arithmetic. In this work, a new linear regression model with interval-valued response and real predictor based on the interval arithmetic is formally described. The least-squares estimation of the model is solved by means of a constrained...

Extensions of previous linear regression models for interval data are
presented. A more flexible simple linear model is formalized. The new model may
express cross-relationships between mid-points and spreads of the interval data
in a unique equation based on the interval arithmetic. Moreover, extensions to
the multiple case are addressed. The asso...

The construction of confidence sets for the parameters of a flexible simple linear regression model for interval-valued random sets is addressed. For that purpose, the asymptotic distribution of the least-squares estimators is analyzed. A simulation study is conducted to investigate the performance of those confidence sets. In particular, the empir...

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, th...

Least-squares estimation of various linear models for interval data has already been considered in the literature. One of
these models allows different slopes for mid-points and spreads (or radii) integrated in a unique equation based on interval
arithmetic. A preliminary study about the construction of confidence regions for the parameters of that...

A generalized simple linear regression statistical/probabilistic model in which both input and output data can be fuzzy subsets of Rp is dealt with. The regression model is based on a fuzzy-arithmetic approach and it considers the possibility of fuzzy-valued random errors. Specifically, the least-squares estimation problem in terms of a versatile m...

The linear relationship between interval-valued random sets can arise in different ways. Recently, a linear model based on
the natural arithmetic for intervals has been studied. In order to test whether the explanatory random set contributes significantly
to explain the response random set through that linear model, an asymptotic testing procedure...

The suitability of the family of d
K
-distances for intervals to quantify and estimate the variability of a random interval with respect to its Aumann expectation
is discussed. To be precise, we will review some properties of the metrics and the associated variance. Then, we will show
that the sample variance is a consistent estimator of the popul...

Simple and multiple linear regression models are considered between variables whose “values” are convex compact random sets
in $${\mathbb{R}^p}$$ , (that is, hypercubes, spheres, and so on). We analyze such models within a set-arithmetic approach. Contrary to what happens
for random variables, the least squares optimal solutions for the basic affin...