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The main aim of this note is to point out by means of counter-examples that some arguments of the proofs of two theorems about a "half variational principle" for multivalued maps, formulated recently by Vivas and Sirvent [Metric entropy for…
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…
Let $V$ be a locally bounded measurable function such that $e^{-V}$ is bounded and belongs to $L^1(dx)$, and let $\mu_V(dx):=C_V e^{-V(x)} dx$ be a probability measure. We present the criterion for the weighted Poincar\'{e} inequality of…
Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for…
In this paper, we introduce and analyze several different notions of Weyl almost periodic functions and Weyl ergodic components in Lebesgue spaces with variable exponent $L^{p(x)}.$ We investigate the invariance of (asymptotical) Weyl…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
We consider the bifurcation problem u'' + \lambda u = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue \lambda. A new derivation of a variational principle for the lowest…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…
The variational method employing the amplitude and width as collective coordinates of the Klein-Gordon oscillon leads to a dynamical system with unstable periodic orbits that blow up when perturbed. We propose a multiscale variational…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
Let $T\subset\mathbb{R}$, $M$ be a metric space with metric $d$, and $M^T$ be the set of all functions mapping $T$ into $M$. Given $f\in M^T$, we study the properties of the approximate variation $\{V_\varepsilon(f)\}_{\varepsilon>0}$,…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
We prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions…
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…
We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal invariant measure, which may be derived via…