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Using the variational formula for operator product coefficients a method for perturbative calculation of the short-distance expansion of the Spin-Spin correlation function in the two dimensional Ising model is presented. Results of explicit…

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and…

Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…

We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Mat\'ern class. The multiscale approximation is constructed through a sequence of residual corrections, where radial…

In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…

To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

In this article we will analyse how to compute the contribution of each input value to its aggregate output in some nonlinear models. Regression and classification applications, together with related algorithms for deep neural networks are…

Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…

In this article, we study the problem of variable screening in multiple nonparametric regression model. The proposed methodology is based on the fact that the partial derivative of the regression function with respect to the irrelevant…

In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…

This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…

Quark distribution and spectator functions are estimated in a diquark spectator model. The representation of the functions in terms of non-local operators together with the rather simple model allow estimates for the yet experimentally…

In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…

We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…