相关论文: Free-Knot Spline Approximation of Stochastic Proce…

In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…

This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary $L_p$-norms ($1 \leq p \leq \infty)$. We prove the existence of best approximations und derive…

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…

In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and…

The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…

The main purpose of this paper is to give a solution to a long-standing unsolved problem concerning the pathwise strong approximation of stochastic differential equations with respect to the global error in the $L_{\infty}$-norm. Typically,…

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions. We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity…

The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…

We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…

In thermally fluctuating long linear polymeric chain in solution, the ends come from time to time into a direct contact or a close vicinity of each other. At such an instance, the chain can be regarded as a closed one and thus will form a…

Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…

We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

In many applications that involve the inference of an unknown smooth function, the inference of its derivatives will often be just as important as that of the function itself. To make joint inferences of the function and its derivatives, a…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…

Kolmogorov-Arnold Neural Networks (KANs) have gained significant attention in the machine learning community. However, their implementation often suffers from poor training stability and heavy trainable parameter. Furthermore, there is…

In this paper we propose a model selection approach to fit a regression model using splines with a variable number of knots. We introduce a penalized criterion to estimate the number and the position of the knots where to anchor the splines…