相关论文: On objective and strong objective consistent estim…
It is introduced a certain approach for equipment of an arbitrary set of the cardinality of the continuum by structures of Polish groups and two-sided (left or right) invariant Haar measures. By using this approach we answer positively…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…
We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the…
In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common…
We study strong types and Galois groups in model theory from a topological and descriptive-set-theoretical point of view, leaning heavily on topological dynamical tools. More precisely, we give an abstract (not model theoretic) treatment of…
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
The notion of strong measure zero is studied in the context of Polish groups. In particular, the extent to which the theorem of Galvin, Mycielski and Solovay holds in the context of an arbitrary Polish group is studied. Hausdorff measure…
The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…
A subset $X$ of a Polish group $G$ is \emph{Haar null} if there exists a Borel probability measure $\mu$ and a Borel set $B$ containing $X$ such that $\mu(gBh)=0$ for every $g,h \in G$. A set $X$ is \emph{Haar meager} if there exists a…
We study the descriptive complexity of sets of points defined by placing restrictions on statistical behaviour of their orbits in dynamical systems on Polish spaces. A particular examples of such sets are the set of generic points of a…
Given an observational study with $n$ independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit using only one $p$-dimensional sample per unit containing covariates, interventions, and outcomes.…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
A key condition for obtaining reliable estimates of the causal effect of a treatment is overlap (a.k.a. positivity): the distributions of the features used to perform causal adjustment cannot be too different in the treated and control…
In this work, we show that if $f$ is a uniformly continuous map defined over a Polish metric space, then the set of $f$-invariant measures with zero metric entropy is a $G_\delta$ set (in the weak topology). In particular, this set is…
We study a nonparametric regression model for sample data which is defined on an $N$-dimensional lattice structure and which is assumed to be strong spatial mixing: we use design adapted multidimensional Haar wavelets which form an…
Descriptive set theory was originally developed on Polish spaces. It was later extended to $\omega$-continuous domains [Selivanov 2004] and recently to quasi-Polish spaces [de Brecht 2013]. All these spaces are countably-based. Extending…
We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…