1,241 Results Found

This study quantitatively approximates the unit operator using three types of multivariate, overactivated, and spiked convolution operators. The core of these operators is a multivariate “cusp” kernel, which acts as a novel, compact-suppo...

Here we study the quantitative multivariate approximation of perturbed hyperbolic tangent-activated singular integral operators to the unit operator. The engaged neural network activation function is both parametrized and deformed, and the related ke...

In this article, we employ the uniform and $L_p$, $1\le p<\infty$ approximation properties of general smooth multivariate singular integral operators over ${\mathbb{R}}^N$, $N\ge 1$. It is a trigonometric relief approach with detailed applications to the correspondin...

In this article, we introduce, for the first time, multivariate symmetrized and perturbed hyperbolic tangent-activated convolution-type operators in three forms. We present their approximation properties, that is, their quantitative convergence to th...

This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of ${\mathbb{R}}^{\overline{N}}$, $\overline{N}\in \mathbb{N}$. Moreover, we consider the case of approximation employing...

In this article, we study the multivariate quantitative smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent activation...

In this work we study the univariate and multivariate quantitative approximation by multi-composite Kantorovich–Choquet-type quasi-interpolation neural network operators with respect to the supremum norm. This is achieved with rates via the fir...

In this study, we develop a class of multivariate HHC-type operators generated by adjustable half-hyperbolic tangent activation functions and a symmetrized kernel structure. The analysis is carried out within the classical framework of positive linea...

We develop a technique for obtaining the fourth moment bound on the normal approximation of F, where F is an ${\mathbb{R}}^d$-valued random vector whose components are functionals of Gaussian fields. This study transcends the case of vectors of multiple stochastic...

In the present paper, we propose a large sample asymptotic approximation for the sampling and posterior distributions of differential entropy when the sample is composed of independent and identically distributed realization of a multivariate normal...

Considering the stability and safety of industrial production, the open-loop system cannot meet the requirements of industrial production, so more and more attention has been paid to multivariable closed-loop system identification. This study focuses...

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain M...

This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is repres...

We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby nor...

Unsupervised feature selection seeks to identify informative, nonredundant features without using class labels. Motivated by Fano’s inequality, we use the entropy of the selected feature subset as a task-agnostic heuristic for its information c...

In this article we present the multivariate approximation of time splitting random functions defined on a box or ${\mathbb{R}}^N,N\in \mathbb{N},$ by neural network operators of quasi-interpolation type. We achieve these approximations by obtaining quantitative-type Jack...

A system of simultaneous multi-variable nonlinear equations can be solved by Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superline...

The Taylor approximation theorem is a fundamental tool in numerical analysis, providing a local polynomial representation of smooth functions. In practical computations, a function f is approximated by a finite Taylor polynomial $P_n$, and controlling t...

This work suggests a solution for the output reference model (ORM) tracking control problem, based on approximate dynamic programming. General nonlinear systems are included in a control system (CS) and subjected to state feedback. By linear ORM sele...

This paper studies the uniqueness of the bounded solution to a new Cauchy problem of the fractional nonlinear partial integro-differential equation based on the multivariate Mittag–Leffler function as well as Banach’s contractive principl...

Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the “curse of dimensionality”, since the...

Modeling loss data is a crucial aspect of actuarial science. In the insurance industry, small claims occur frequently, while large claims are rare. Traditional heavy-tail distributions, such as Weibull, Log-Normal, and Inverse Gaussian distributions,...

In this paper, we study the probabilistic Gel’fand $\left(N,\delta \right)$-width of multivariate Sobolev spaces $M{W}_2^r\left({\mathbb{T}}^d\right)$ with mixed derivative that are equipped with Gaussian measure $\mu$ in $L_q\left({\mathbb{T}}^d\right)$. The sharp asymptotic estimates ar...

Accurate forecasting of high-resolution particulate matter 2.5 (PM_2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approa...

Multivariate nonlinear mixed-effects models (MNLMM) have received increasing use due to their flexibility for analyzing multi-outcome longitudinal data following possibly nonlinear profiles. This paper presents and compares five different iterative a...

In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and...

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries a...

This paper aims at presenting a novel effective approach to probabilistic analysis of distribution power grid with high penetration of PV sources. The novel method adopts a Gaussian Mixture Model for reproducing the uncertainty of correlated PV sourc...

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a me...

In this study, two new integrated control charts, named $T^2$-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be sp...

The complexity of estimating multivariate GARCH models increases significantly with the increase in the number of asset series. To address this issue, we propose a general regularization framework for high-dimensional GARCH models with BEKK represent...

We investigate $L_2$-approximation problems in the worst case setting in the weighted Hilbert spaces $H\left(K_{R_{d,\mathit{\alpha },\mathit{\gamma }}}\right)$ with weights $R_{d,\mathit{\alpha },\mathit{\gamma }}$ under parameters $1\ge {\gamma }_1\ge {\gamma }_2\ge \cdots \ge 0$ and $1<{\alpha }_1\le {\alpha }_2\le ;$...

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank...

The development of regression models for composite distributions has received insufficient attention in the literature. The purpose of this research is to provide maximum likelihood (ML) and approximate Bayesian computation (ABC) estimators for the p...

In this paper, we determine the stability of multivariable bi-Jensen functional equation $mnf\left({\displaystyle \frac{x_1+\cdots +x_m}{m}},{\displaystyle \frac{y_1+\cdots +y_n}{n}}\right)={\sum }_{i=1}^m{\sum }_{j=1}^{n}f(x_i,y_j)$ in Banach spaces. We establish a Hyers-Ulam-Rassias stability result using a direct method and a fixe...

Good air quality is essential for both human beings and the environment in general. The three most harmful air pollutants are nitrogen dioxide (NO₂), ozone (O₃) and particulate matter. Due to the high cost of monitoring stations, few examples of this...

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian discrepancy measure used in testing precise statistical hypotheses. In particular, we derive results on third-order asymptotic appr...

Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this cl...

It is well known that feed-forward neural networks can be used for approximation to functions based on an appropriate activation function. In this paper, employing a new sigmoidal function with a parameter for an activation function, we consider a co...

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the stru...

Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relatio...

This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis funct...

This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Di...

In this article, we give the sharp bounds of probabilistic Kolmogorov $\left(N,\delta \right)$-widths and probabilistic linear $\left(N,\delta \right)$-widths of the multivariate Sobolev space $W_2^A$ with common smoothness on a $S_q$ norm equipped with the Gaussian measure $\mu$, where...

There has been a considerable evolution of the theory of fractal interpolation function (FIF) over the last three decades. Recently, we introduced a multivariate analogue of a special class of FIFs, which is referred to as $\alpha$-fractal functions, from t...

In order to improve the accuracy of wind power prediction (WPP), we propose a WPP based on multivariate phase space reconstruction (MPSR) and multivariate linear regression (MLR). Firstly, the multivariate time series (TS) are constructed through rea...

The purpose of this paper is fourfold: (i) to introduce and study the Euler–Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemann...

The paper develops applications of symmetric orbit functions, known from irreducible representations of simple Lie groups, in numerical analysis. It is shown that these functions have remarkable properties which yield to cubature formulas, approximat...

Copulas are widely used in financial economics, as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes a “natural copula” concept that minimizes the Wasserstein distance bet...

This work provides exact and analytical approximate solutions for a non-linear time-fractional generalized biology population model (FGBPM) with suitable initial data under the time-Caputo fractional derivative, in view of a novel effective and appli...