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The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
Fiducial inference was introduced in the first half of the 20th century by Fisher (1935) as a means to get a posterior-like distribution for a parameter without having to arbitrarily define a prior. While the method originally fell out of…
In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are close to Gaussian distribution but have a longer tail. Their…
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…