Related papers: Nonstandard Analysis: Its Creator and Place
The concept of Bohr radius for the class of bounded analytic functions was introduced by Harald Bohr in 1914. His initial result received greater interest and was sharpened-refined-generalized by several mathematicians in various…
This paper studies the identification and estimation of a nonparametric nonseparable dyadic model where the structural function and the distribution of the unobservable random terms are assumed to be unknown. The identification and the…
I review the present status of nuclear lattice simulations. This talk is dedicated to the memory of Gerald E. Brown.
This paper is dedicated to the "50 Years of the Relevance Problem" - a long-neglected topic that begs attention from practical statisticians who are concerned with the problem of drawing inference from large-scale heterogeneous data.
Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing…
Artin-Schelter regular algebras can be thought of as noncommutative versions of commutative polynomial rings, modeled after the special homological properties polynomial rings have as graded rings. First defined by Artin and Schelter in…
Let $^*\mathbb{R}$ be a nonstandard extension of $\mathbb{R}$ and $\rho$ be a positive infinitesimal in $^*\mathbb{R}$. We show how to create a variety of isomorphisms between A. Robinson's field of asymptotic numbers $^\rho\mathbb{R}$ and…
Inflation is considered one of the cornerstones of modern cosmology. However, the account of the origin of cosmic structure, as provided by the standard inflationary paradigm, is not fully satisfactory. The fundamental issue is the…
It is with pleasure and pride that I introduce this special section in honor of Ingram Olkin. This tribute is especially fitting because, among the many profound and far-reaching contributions that he has made to our profession, Ingram…
Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…
In this paper, we analyze a sample of clippings from paintings by the late artist Bob Ross. Previous work focused on the qualitative themes of his paintings (Hickey, 2014); here, we expand on that line of research by considering the…
Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a…
The momentum operator representation of nonrelativistic anyons is developed in the Chern - Simons formulation of fractional statistics. The connection between anyons and the q-deformed bosonic algebra is established.
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
This work presents a geometric refinement of the classical Cram\'er--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model…
Certain operator-valued functions and new generating structures (instead of generating functionals) are proposed for the analysis of equations for n-point information (n-pi). Some remarks are made concerning the intertwining of linearity…
A Bayesian nonparametric approach to the study of species diversity based on choosing a random discrete distribution as a prior model for the unknown relative abundances of species has been recently introduced in Lijoi et al. (2007, 2008).…
Interpretation of a structure $\mathbb A$ in $\mathbb B$ allows to produce structures elementarily equivalent to $\mathbb A$ given those elementarily equivalent to $\mathbb B$. In particular, interpretation of the free group in $\mathbb N$…
In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error…