Lasso Estimation of an Interval-Valued Multiple Regression Model

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary problem and using Lemke's algorithm to solve it. Due to the irrelevance of certain cross-relationships, an alternative estimation process, the LASSO (Least Absolut Shrinkage and Selection Operator), is developed. A comparative study showing the differences between the proposed estimators is provided

On special partitions of [0, 1] and lineability within families bounded variation functions

We show that there exists large algebraic structures (vector spaces, algebras, closed subspaces, etc.) formed entirely (except for 0), on one hand, by singular, nowhere monotonic functions on [0, 1] and, on the other hand, by absolutely continuous nowhere monotonic functions. Several tools, of independent interest, related to obtaining special partitions of R into uncountable collections will be provided and used. The results obtained in this note are either new or improved version of already existing ones.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEMinisterio de Ciencia e Innovación (MICINN)Junta de AndalucíaWISS 2025 projectunpu

Lineability, differentiable functions and special derivatives

The present work either extends or improves several results on lineability of differentiable functions and derivatives enjoying certain special properties. Among many other results, we show that there exist large algebraic structures inside the following sets of special functions: (1) The class of differentiable functions with discontinuous derivative on a set of positive measure, (2) the family of differentiable functions with a bounded, non-Riemann integrable derivative, (3) the family of functions from (0, 1) to R that are not derivatives, or (4) the family of mappings that do not satisfy Rolle’s theorem on real infinite dimensional Banach spaces. Several examples and graphics illustrate the obtained results

Lineability and integrability in the sense of Riemann, Lebesgue, Denjoy, and Khintchine

In this paper, we continue the ongoing research on lineability related questions. On this occasion, we shall consider (among others) the classes of integrable functions (in the sense of Riemann, Lebesgue, Denjoy, and Khintchine), improving some already known results and expanding the study of lineability to other famous integrable classes never considered before

Highly tempering infinite matrices II: From divergence to convergence via Toeplitz–Silverman matrices

It was recently proved [6] that for any Toeplitz{Silverman matrix A, there exists a dense linear subspace of the space of all sequences, all of whose nonzero elements are divergent yet whose images under A are convergent. In this paper, we improve and generalize this result by showing that, under suitable assumptions on the matrix, there are a dense set, a large algebra and a large Banach lattice consisting (except for zero) of such sequences. We show further that one of our hypotheses on the matrix A cannot in general be omitted. The case in which the field of the entries of the matrix is ultrametric is also considered

A typical copula is singular

We present Baire category results in the class of bivariate copulas (or, equivalently, doubly stochastic probability measures) endowed with two different metrics under which the space is complete. Main content of the paper is that, in the sense of Baire categories with respect to the topology induced by the uniform metric, the family of absolutely continuous copulas is of first category, whereas the family of purely singular copulas is co-meager and, hence, of second category. Moreover, several other popular dense sub-classes of copulas are considered, like shuffles of Min and checkerboard copulas

Spatially homogeneous copulas

We consider spatially homogeneous copulas, i.e. copulas whose corresponding measure is invariant under a special transformations of [0 , 1] 2, and we study their main properties with a view to possible use in stochastic models. Specifically, we express any spatially homogeneous copula in terms of a probability measure on [0, 1) via the Markov kernel representation. Moreover, we prove some symmetry properties and demonstrate how spatially homogeneous copulas can be used in order to construct copulas with surprisingly singular properties. Finally, a generalization of spatially homogeneous copulas to the so-called (m, n)-spatially homogeneous copulas is studied and a characterization of this new family of copulas in terms of the Markov ∗ -product is established