The solution of many inference problems involves random processes that summarize or describe the information that is available. Important examples of these processes are empirical processes constructed from random samples,
estimated residuals processes, or cumulative estimated residuals processes in regression models or in the analysis of time series. In some cases, when the size n of the data sets tends to infinity, these processes have Gaussian limits,
and it is convenient to test the effects of various alternative models on the asymptotic distributions by using contiguity and applying Le Cam’s Third Lemma.

My research activity  during my post-doc at Universitat de Barcelona (1993-1996) and later on at Instituto Venezolano de Investigaciones Científicas (1997-2003) and Universidad de Valladolid (2003-2009)
consisted in developing transformations applicable to these processes and their Gaussian limits, which without losing the ability to describe all kinds of alternatives, help to focus the user's attention on certain privileged alternatives
such as symmetry, or changes in kurtosis .  Most of this work was done with the collaboration of E.M. Cabaña (UdelaR, Uruguay). The inference procedures that we developed can be expressed in terms of goodness-of-fit tests
where the hypothesis is that a certain distribution (belonging to a parametric family perhaps) is adequate to describe the behavior of certain elements that characterize the empirical information. The work developed through these years ended
up in a common procedure to deal with all the previously published examples. The main tools are the Transformed Empirical Processes (PETs), introduced in Ann. Statist. 24, (1996). The use of PETs allowed to selectively optimize the power of tests of the Kolmogorov-Smirnov type against families of local alternatives,
consistent and asymptotically equivalent to the Likelihood Ratio Test. We developed tests based on quadratic functionals of TEPs for compound hypotheses, asymptotically as good as the former ones, but more powerful for small samples.
The tests were generalized to data with different dependency structures. A nice property is that they are all distribution free, and all of them, have the same known asymptotic distribution. 
This provides a unified testing setup, even though for practical purposes, the asymptotic distribution provides less powerful tests than its Monte-Carlo counterpart. This line of work produced 15 articles in peer reviewed journals and conferences,
including 3 in Ann.Statist. and have been presented in numerous invited or contributed conferences, and a textbook . We have recently resumed the study of g-o-f tests with the intention to include other null families.
Another widely used technique for goodness-of fit testing is the use of empirical Laplace or Fourier transforms. I have a paper with A.J.Quiroz. We have also worked in developing two sample tests for functional data.Around 2010, E.M. Cabaña and myself began a collaboration with A. Arratia, which derived in a series of papers on generalized Ornstein-Uhlenbeck processes and other extensions of CARMA processes, having defined an embedding in law of classical ARMA
into a continuous time stationary family of processes, which, when sampled at discrete times have not only the moments of an ARMA, but also the same finite distributions.
In collaboration with P.Puig, D. Moriña and A. Fernández, we  studied the possible under-reporting of count time series. We published 2 papers in Statistics in Medicine dealing with the under-reporting of epidemiological and gender violence data.  We applied similar techniques to the COVID data in Spain. We have published five papers. I also taught a course within the Ecodep  project in which I participate.
I have also worked in several financial applications resulting in conference papers, a book chapter on sentiment indicators, an application to clustering of time series, and a paper derived from the Ph.D. Thesis of my former student G. Junike.

I have always had model-driven interests, however, the possibility of finding interactions between my theoretical background on empirical processes and the outcome of Neural networks in order to study variable importance drives my current research interest.