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In this paper, we establish two different results. The first result is a characterization theorem saying that if the stationary state probabilities for originally described Markovian discriminatory processor sharing (DPS) system have a…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number…
This article is a discussion of some characteristic properties in connection with global models, particularly for the application of prediction, such as the approximation property, the interpolation property and the transmission property.
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…
We consider two variants of those Abelian groups with all proper characteristic subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
Let $G$ be a finite group. We study the generalized character defined by $\Xi(g)=|G|o(g)$, for $g\in G$, which is closely related to a function that has been very studied recently from a group theoretical point of view.
We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions,…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
In this paper, we derive eight basic identities of symmetry in three variables related to generalized Bernoulli polynomials and generalized power sums. All of these are new, since there have been results only about identities of symmetry in…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such…
Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions for estimating the statistical significance of discovery using the asymptotic approximations of Wilks and…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
Motivated by Emmanuel Kowalski's exponential sums over definable sets in finite fields, we generalize Ax's theorem on pseudo-finite fields to a continuous-logic setting allowing for an additive character. The role played by Weil's Riemann…