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new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper provides a circular version of the well-known Sheather and Jones bandwidths (J R Stat Soc Ser B Stat Methodol 53(3):683–690, 1991. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x), with direct and solve-the-equation plug-in rules. Theoretical support for our developments, related to the asymptotic mean squared error of the estimator of the density, its derivatives, and its functionals, for circular data, are provided. The proposed selectors are compared with previous data-based smoothing parameters for circular kernel density estimation. This paper also contributes to the study of the optimal kernel for circular data. An illustration of the proposed plug-in rules is also shown using real data on the time of car accidents

In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli–Arzel`a and Kolmogorov–Riesz theorems, as well as their applications to Stieltjes-Sobolev spaces and decomposable functions.

Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for anAtlantic climate location, spring and fall seasons should present amild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response)would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya–Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves.

In this paper, we obtain an explicit expression for the Green’s function of a certain type of systems of differential equations subject to non-local linear boundary conditions. In such boundary conditions, the dependence on certain parameters is considered. The idea of the study is to transform the given system into another first-order differential linear system together with the two-point boundary value conditions. To obtain the explicit expression of the Green’s function of the considered linear system with non-local boundary conditions, it is assumed that the Green’s function of the homogeneous problem, that is, when all the parameters involved in the non-local boundary conditions take the value zero, exists and is unique. In such a case, the homogeneous problem has a unique solution that is characterized by the corresponding Green’s function g. The expression of the Green’s function of the given system is obtained as the sum of the function g and a part that depends on the parameters involved in the boundary conditions and the expression of function g. The novelty of our work is that in the system to be studied, the unknown functions do not appear separated neither in the equations nor in the boundary conditions. The existence of solutions of nonlinear systems with linear non-local boundary conditions is also studied. We illustrate the obtained results in this paper with examples.

Based on Holler (1982), Colomer and Martínez (1995), and Armijos-Toro et al. (2021), we propose two power indices to measure the influence of the players in these classes of weighted majority games in partition function form. We compare the new power indices with their original versions on the class of games in characteristic function form. Finally, we use both new power indices and the two power indices for games in partition function form studied in Alonso-Meijide et al. (2017) to study the distribution of power in the National Assembly of Ecuador that emerged after the elections of February 7, 2021.

A new lack-of-fit test for censored quantile regression models with multiple or even high-dimensional covariates will be presented. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates. The test is then adapting the ideas presented in [1], to cope with high-dimensional covariates, to the test proposed by [2]. The limit distribution of the empirical process associated with the test statistic will be shown. Furthermore, in order to approximate the critical values of the test, a bootstrap mechanism is used, which is similar to the proposal developed in [3]. In addition, an extensive simulation study and an interesting real data application will be presented in order to show the behaviour of the new test in practice

This paper presents new specification tests for a general synchronous additive concurrent model formulation. As a novelty, our proposal does not require a preliminary model or error structure estimation. No tuning parameters are involved either. We develop a suitable test statistic using the martingale difference divergence coefficient. As a result, this statistic measures the departure from the conditional mean independence in the concurrent model framework, considering the information of all observed time instants. In particular, global as well as partial dependence tests are introduced. Then, we allow one to quantify the effect of a group of covariates or to apply covariates selection one by one. We obtain its asymptotic distribution under the null and propose a bootstrap algorithm to compute the p-values in practice. Through simulations, we illustrate our method, and its performance is compared to existing competitors. In addition, we use this in the analysis of three real datasets related to gait data, flu activity, and casual bike rentals

In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces via resolvent operators. Initially, we prove the existence of mild solution for the system is established by using Mönch fixed point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results includes continuous dependence of solutions on initial conditions, exponential stability and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results

This paper addresses two sampling methodologies to respectively estimate the Owen value and the Banzhaf–Owen value for TU-games with a priori unions. Both proposals are based on stratified sampling on the set of those coalitions that are compatible with the system of unions according to their cardinalities. These sampling methodologies are analysed in terms of the theoretical properties and of the establishment of bounds for the absolute error from a statistical point of view. Finally, we evaluate the performance of these tools on several real well-known examples in the literature

This is a didactic proposal on how to introduce the Newton integral in just three or four sessions in elementary courses. Our motivation for this paper were Talvila’s work on the continuous primitive integral and Koliha’s general approach to the Newton integral. We introduce it independently of any other integration theory, so some basic results require somewhat nonstandard proofs. As an instance, showing that continuous functions on compact intervals are Newton integrable (or, equivalently, that they have primitives) cannot lean on indefinite Riemann integrals. Remarkably, there is a very old proof (without integrals) of a more general result, and it is precisely that of Peano’s existence theorem for continuous nonlinear ODEs, published in 1886. Some elements in Peano’s original proof lack rigor, and that is why his proof has been criticized and revised several times. However, modern proofs are based on integration and do not use Peano’s original ideas. In this note we provide an updated correct version of Peano’s original proof, which obviously contains the proof that continuous functions have primitives, and it is also worthy of remark because it does not use the Ascoli-Arzelà theorem, uniform continuity, or any integration theory

In this paper, we introduce a notion of mergeable weighted majority games with the aim of providing the first characterization of the Colomer–Martínez power index (Colomer and Martínez in J Theor Polit 7(1):41–63, 1995). Furthermore, we define and characterize a new power index for the family of weighted majority games that combines ideas of the Public Good (Holler in Polit Stud 30(2):262–271, 1982) and Colomer–Martínez power indices. Finally, we analyze the National Assembly of Ecuador using these and some other well-known power indices

Resource assignment and scheduling models provides an automatic and fast decision support system for wildfire suppression logistics. However, this process generates challenging optimization problems in many real-world cases, and the computational time becomes a critical issue, especially in realistic-size instances. Thus, to overcome that limitation, this work studies and applies a set of decomposition techniques such as augmented Lagrangian, branch and price, and Benders decomposition’s to a wildfire suppression model. Moreover, a reformulation strategy, inspired by Benders’ decomposition, is also introduced and demonstrated. Finally, a numerical study comparing the behavior of the proposals using different problem sizes is conducted

In this paper we introduce RAPOSa, a global optimization solver specifically designed for (continuous) polynomial programming problems with box-constrained variables. Written entirely in C++, RAPOSa is based on the Reformulation-Linearization (Sherali and Tuncbilek in J Glob Optim 103:225–249, 1992). We present a description of the main characteristics of RAPOSa along with a thorough analysis of the impact on its performance of various enhancements discussed in the literature, such as bound tightening and SDP cuts. We also present a comparative study with three of the main state-of-the-art global optimization solvers: BARON, Couenne and SCIP

In this paper, we introduce a two-point nonlinear boundary value problem for a finite fractional difference equation. An associated Green’s function is constructed as a series of functions and some of its properties are obtained. Some existence results are deduced from fixed point theory and lower and upper solutions

We obtain the analytical solutions in implicit form of a tumor cell population differential equation with strong Allee effect. We consider the ordinary case and then a fractional version. Some particular cases are plotted

We solve a logistic differential equation for generalized proportional Caputo fractional derivative. The solution is found as a fractional power series. The coefficients of that power series are related to the Euler polynomials and Euler numbers as well as to the sequence of Euler’s fractional numbers recently introduced. Some numerical approximations are presented to show the good approximations obtained by truncating the fractional power series. This generalizes previous cases including the Caputo fractional logistic differential equation and Euler’s numbers

In this paper, we investigate the solution of multi-term time-space fractional partial delay differential-algebraic equations (MTS-FPDDAEs) with Dirichlet boundary conditions defined on a finite domain. We use Laplace transform method to give the solutions of multi-term time fractional delay differential-algebraic equations (MTS-FDDAEs). Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the MTS-FPDDAEs into the MTS-FDDAEs. By applying our obtained solutions to the resulting MTS-FDDAEs, the desired analytical solutions of the MTS-FPDDAEs are obtained. Finally, we give the solutions of some special cases

The first part of this work reviews several mathematical programming models dedicated to resource allocation and planning problems in the context of extinguishing large forest fires. These problems have been studied as part of the research projects Lumes and Enjambre, which involve both the public and private sectors in Spain. The objective of Lumes and Enjambre is to develop advanced technologies for fighting forest fires. Moreover, the projects address other tasks such as the design of algorithms to prevent aircraft collisions and estimating the perimeters of forest fires using techniques such as estimating sets from thermal images. The second part of this work is focused on the R package and corresponding graphic interface, Wildfire Resources Management (wrm), which are designed to offer a user-friendly model interface in terms of the introduction of the necessary data, resolution, and presentation of the results, according to the needs of the interlocutors in the company dedicated to the extinction of forest fires. The auxiliary package uses various solvers, such as symphony and gurobi. This work presents the various components of wrm (which can be viewed in the GitHub repository), a computational study, and a procedure for its use.

In this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder’s fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our results

In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convex

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation of the Dirichlet conditions by considering a homogeneous Dirichlet-type condition at one extreme of the interval and an integral operator on the other one. We obtain the expression of the Green’s function related to the linear part of the equation and characterize its constant sign. Such a property will be fundamental to deduce the existence of solutions of the nonlinear problem. The results hold from fixed point theory applied to related operators defined on suitable cones

The aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations

Highest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismology

Ecological Risk Assessment faces the challenge of determining the impact of invasive species on biodiversity conservation. Although many statistical methods have emerged in recent years in order to model the evolution of the spatio-temporal distribution of invasive species, the notion of extent of occurrence, formally defined by the International Union for the Conservation of Nature, has not been properly handled. In this work, a novel and flexible reconstruction of the extent of occurrence from occurrence data will be established from nonparametric support estimation theory. Mathematically, given a random sample of points from some unknown distribution, we establish a new data-driven method for estimating its probability support S in general dimension. Under the mild geometric assumption that S is r−convex, the smallest r−convex set which contains the sample points is the natural estimator. A stochastic algorithm is proposed for determining an optimal estimate of r from the data under regularity conditions on the density function. The performance of this estimator is studied by reconstructing the extent of occurrence of an assemblage of invasive plant species in the Azores archipelago

In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have one solution under the Osgood condition, or even, the Montel–Tonelli condition. We also explore some results guaranteeing the existence of solution under these conditions. Along the way, we obtain some interesting properties for the Lebesgue– Stieltjes integral associated to a finite sum of nondecreasing and left–continuous maps, as well as a characterization of the pseudometric topologies defined by this type of maps

In this article we combine the study of solutions of PDEs with the study of asymptotic properties of the solutions via compactification of the domain. We define new spaces of functions on which study the equations, prove a version of Ascoli–Arzelà Theorem, develop the fixed point index results necessary to prove existence and multiplicity of solutions in these spaces and also illustrate the applicability of the theory with an example

In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of a function of controlled variation, a characterization of precompact sets of g-continuous functions, and an explicit expression of g-exponential maps. Finally, we prove a Peano-type existence result and apply it to a model of fluid stratification on buoyant miscible jets and plumes.

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist in replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new results for the existence of extremal solutions for discontinuous Stieltjes differential equations. In particular, we prove that the pointwise infimum of upper solutions of a Stieltjes differential equation is the minimal solution under certain hypotheses. These results can be adapted to the context of both difference equations and impulsive differential equations

In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multipoint second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a new perturbation technique, which allows obtaining an existence result and a localization theorem. Our hypotheses are clearly much less restrictive than those existent in the literature and, moreover, they can be applied to higher-order, resonant or nonresonant, boundary value problems defined on the half-line or even on the real line

We improve some comparison results for the periodic boundary value problem related to a first-order differential equation perturbed by a functional term. The comparison results presented cover many cases as differential equations with delay, differential equations with maxima and integro-differential equations. The interesting case of functional perturbation with piecewise constant arguments is also analyzed.

This paper is concerned with the existence of solutions of an inverse discrete problem with sign-changing nonlinearity. This kind of problems includes, as a particular case, nth order difference equations coupled with suitable conditions on the boundary of the interval of definition. It would be valid for the case in which the related Green’s function is positive on a subset of its rectangle of definition. The existence results follow from spectral theory, as an application of the Krein–Rutman theorem and by means of degree theory

In this paper, we present sufficient criteria ensuring the existence and uniqueness of solutions for nonlinear impulsive multi-order Caputo-type generalized fractional differential equations supplemented with nonlocal integro-initial value conditions involving generalized fractional integrals. Extremal solutions for the given problem are also discussed. The main tools of our study include Krasnoselskii’s fixed point theorem, Banach contraction mapping principle and monotone iterative technique. Examples are constructed for illustrating the obtained results

We present a new formula that makes it possible to get sharp global stability results for one-dimensional discrete-time models in an easy way. In particular, it allows to show that the local asymptotic stability of a positive equilibrium implies its global asymptotic stability for a new family of difference equations that finds many applications in population dynamics, economic models, and also in physiological processes governed by delay differential equations. The main ingredients to prove our results are the Schwarzian derivative and some dominance arguments

The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. For real random variables, this task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals for testing the number of modes provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented together with a revision on the previous proposals. The new method is compared with the existing ones in an extensive simulation study, showing a superior behaviour, with good calibration and power results. Theoretical justification for its performance is also obtained. A real data example on philatelic data is also included for illustration purposes, revising previous approaches and discussing the results with the new procedure

In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also given

Quantile regression methods are evaluated for computing predictions and prediction intervals of NOx concentrations measured in the vicinity of the power plant in As Pontes (Spain). For these data, smaller prediction errors were obtained using methods based on median regression compared with mean regression. A new method to construct prediction intervals involving median regression and bootstrapping the prediction error is proposed. This new method provides better coverage for NOx data compared with classical and bootstrap prediction intervals based on mean regression, as well as simpler prediction intervals based on quantile regression. A simulation study illustrates the features of this proposed method that lead to a better performance for obtaining prediction intervals for these particular NOx concentration data, as well as for any other environmental dataset that do not meet assumptions of homoscedasticity and normality of the error distribution

This paper considers the problem of variable selection when some of the variables have a functional nature and can be mixed with other type of variables (scalar, multivariate, directional, etc). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model. For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, …) of each variable. The algorithm have showed quite promising results when applied to real data sets

The maximum depth classifier was the first attempt to use data depths instead of multivariate raw data in classification problems. Recently, the DD-classifier has addressed some of the serious limitations of this classifier but issues still remain. This paper aims to extend the DD-classifier as follows: first, by enabling it to handle more than two groups; second, by applying regular classification methods (such as kNN, linear or quadratic classifiers, recursive partitioning, etc) to DD-plots, which is particularly useful, because it gives insights based on the diagnostics of these methods; and third, by integrating various sources of information (data depths, multivariate functional data, etc) in the classification procedure in a unified way. This paper also proposes an enhanced revision of several functional data depths and it provides a simulation study and applications to some real data sets

We deal with some generalizations on a Black-Scholes model arising in financial mathematics. As a novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large class of problems involving Black-Scholes equation. Our main results involve the existence of extremal solutions in presence of lower and upper solutions. Some examples of applications are provided too.

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.

In the present work, we consider a boundary value problem with gluing conditions of an integral form for the parabolic-hyperbolic type equation. We prove that the considered problem has the Volterra property. The main tools used in the work are related to the method of the integral equations and functional analysis.

A monotone iterative technique is applied to prove the existence of the extremal positive pseudosymmetric solutions for a three-point second-order p-Laplacian integrodifferential boundary value problem.