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We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…

Statistical Mechanics · Physics 2008-12-10 Raymond J. Hawkins , B. Roy Frieden

We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…

Probability · Mathematics 2023-11-03 Gilles Germain , Yvik Swan

We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of Gaunt, Mijoule and Swan \cite{gms18}. This…

Probability · Mathematics 2020-09-28 Robert E. Gaunt , Guillaume Mijoule , Yvik Swan

A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…

Information Theory · Computer Science 2015-04-28 Giuseppe Toscani

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism.…

Instrumentation and Methods for Astrophysics · Physics 2018-02-28 Thomas D. P. Edwards , Christoph Weniger

A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…

Cosmology and Nongalactic Astrophysics · Physics 2025-12-23 Andrew Repp , Ravi K. Sheth , Istvan Szapudi , Yan-Chuan Cai

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…

Probability · Mathematics 2022-03-15 Thomas Bonis

This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…

Probability · Mathematics 2018-09-12 Peng Chen , Ivan Nourdin , Lihu Xu

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…

Statistics Theory · Mathematics 2021-07-01 Juan Carlos Escanciano

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…

Statistics Theory · Mathematics 2012-07-03 Marc Hallin , Christophe Ley

Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…

Statistics Theory · Mathematics 2024-12-05 Bruno Ebner , Adrian Fischer , Robert E. Gaunt , Babette Picker , Yvik Swan

We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we obtain a characterizing non-local Stein operator which boils…

Probability · Mathematics 2019-04-08 Benjamin Arras , Christian Houdré

We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…

Mathematical Physics · Physics 2025-07-24 Razvan Gabriel Iagar , David Puertas-Centeno , Elio V. Toranzo

We propose probabilistic representations for inverse Stein operators (i.e. solutions to Stein equations) under general conditions; in particular we deduce new simple expressions for the Stein kernel. These representations allow to deduce…

Probability · Mathematics 2019-06-21 Marie Ernst , Gesine Reinert , Yvik Swan

A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…

Information Theory · Computer Science 2010-07-12 Cihan Tepedelenlioglu , Mahesh K. Banavar , Andreas Spanias

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…

Statistics Theory · Mathematics 2021-04-13 Robert E. Gaunt

In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…

Information Theory · Computer Science 2016-02-01 Mark Kelbert , Yuri Suhov , Salimeh Yasaei Sekeh

We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…

Probability · Mathematics 2025-04-14 Chiara Amorino , Arturo Jaramillo , Mark Podolskij

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

Machine Learning · Statistics 2022-03-29 Borja Rodríguez-Gálvez , Germán Bassi , Ragnar Thobaben , Mikael Skoglund

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…

Statistics Theory · Mathematics 2023-06-05 Brodie A. J. Lawson , Kevin Burrage , Kerrie Mengersen , Rodrigo Weber dos Santos