Related papers: Perspective Functions: Properties, Constructions, …
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
A property $(D)$ of subshifts was defined in: Wolfgang Krieger, On $g$-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306 - 316, arXiv:math.DS/0608259. With a view towards a theory of…
In this paper we achieve some new Hadamard type inequalities using elementary well known inequalities for functions whose first derivatives absolute values are s-geometrically and geometrically convex. And also we get some applications for…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data…
The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns…
A representation-theoretic approach to special functions was developed in the 40-s and 50-s in the works of I.M.Gelfand, M.A.Naimark, N.Ya.Vilenkin, and their collaborators. The essence of this approach is the fact that most classical…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
A robust prediction model invoking the Takens embedding theorem, whose \textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz,…
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
We show that many perception tasks, from visual recognition, semantic segmentation, optical flow, depth estimation to vocalization discrimination, are highly redundant functions of their input data. Images or spectrograms, projected into…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…