Related papers: Partial Coherence Estimation via Spectral Matrix S…
Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial…
The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…
Quantum coherence reflects the origin of quantumness and might be capable of extracting the subtle nature of a system. We investigate the ground-state coherence and steered coherence in the Lipkin-Meshkov-Glick model and show that they…
We consider shrinkage estimation of higher order Hilbert space valued Bochner integrals in a non-parametric setting. We propose estimators that shrink the $U$-statistic estimator of the Bochner integral towards a pre-specified target…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
We calculate meson correlators in the epsilon-regime within partially quenched chiral perturbation theory. The valence quark masses and sea quark masses can be chosen arbitrary and all non-degenerate. Taking some of the sea quark masses to…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the…
With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the…