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A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
The problem of error analysis is addressed in stages beginning with the case of uncorrelated parameters and proceeding to the Bayesian problem that takes into account all possible correlations when a great deal of prior information about…
Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$.…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both…
We consider goodness-of-fit methods for multivariate symmetric and asymmetric stable Paretian random vectors in arbitrary dimension. The methods are based on the empirical characteristic function and are implemented both in the i.i.d.…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…
By using the integration by parts formula of a Markov operator, the closability of quadratic forms associated to the corresponding invariant probability measure is proved. The general result is applied to the study of semilinear SPDEs,…
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…