Related papers: A systematic approach to Covariance matrix formula…
The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
We present a calculation of the matter power spectrum covariance matrix ${\rm Cov}(\bf{k}_1,\bf{k}_2)$ that uses power spectrum responses to accurately describe the coupling between large- and small-scale modes beyond the perturbative…
Regression-based optimal fingerprinting techniques for climate change detection and attribution require the estimation of the forced signal as well as the internal variability covariance matrix in order to distinguish between their…
In this study, we aim to develop a new methodology to estimate the cross-correlation function and uncertainties and apply it to the analysis of magnification bias in galaxy surveys. We adopt a new methodological framework that uses a…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
Cosine similarity is an established similarity metric for computing associations on vectors, and it is commonly used to identify related samples from biological perturbational data. The distribution of cosine similarity changes with the…
Upcoming cosmological surveys will achieve increasingly precise constraints in cosmological parameter estimation. To guarantee the robustness of cosmological analyses, it is essential to account for and model systematic effects that can…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…
Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…
Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the…
We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are…
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…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not…
Cosmological weak lensing by the large scale structure of the Universe, cosmic shear, is coming of age as a powerful probe of the parameters describing the cosmological model and matter power spectrum. It complements CMB studies, by…
The stability of model parameters for a class of relativistic energy density functionals, characterized by contact (point-coupling) effective inter-nucleon interactions and density-dependent coupling parameters, is analyzed using methods of…