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We prove characterization theorems for relative entropy (also known as Kullback-Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically…
The well-known Heyde theorem characterizes the Gaussian distributions on the real line by the symmetry of the conditional distribution of one linear form of independent random variables given another. We generalize this theorem to groups of…
We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not qualify as one or the other. Our main result is a characterization theorem, yielding…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about…
We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…
We prove that certain functions involving ratios of Gamma functions and the Psi-function belong to generalized Bernstein classes and new properties of generalized Bernstein functions are given.
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to…
Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
We define and investigate the property of being `exponent-critical' for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups. We…
Explainability methods are often challenging to evaluate and compare. With a multitude of explainers available, practitioners must often compare and select explainers based on quantitative evaluation metrics. One particular differentiator…
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.