Related papers: A generalized quadratic estimate for random field …

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous…

The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…

We show that General Relativity coupled to a quantum field theory generically leads to non-local effects in the matter sector. These non-local effects can be described by non-local higher dimensional operators which remarkably have an…

A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…

Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…

Provided a random realization of the cosmological model, observations of our cosmic neighborhood now allow us to build simulations of the latter down to the non-linear threshold. The resulting local Universe models are thus accurate up to a…

The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…

Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally…

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…

In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear…

The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…

Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The…

The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

An algorithm for non-stationary spatial modelling using multiple secondary variables is developed. It combines Geostatistics with Quantile Random Forests to give a new interpolation and stochastic simulation algorithm. This paper introduces…

We present a first analysis of a nonperturbative approach to quantum gravity based on a representation of quantum field theory in terms of stochastic processes. The stochastic description accommodates a physical Lorentz-invariant…