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The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…
The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes:…
We study improved approximations to the distribution of the largest eigenvalue $\hat{\ell}$ of the sample covariance matrix of $n$ zero-mean Gaussian observations in dimension $p+1$. We assume that one population principal component has…
This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle…
Eigenvalues arising in scattering theory have been envisioned as a potential source of target signatures in nondestructive testing of materials, whereby perturbations of the eigenvalues computed for a penetrable medium would be used to…
Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation…
The analysis of large experimental datasets frequently reveals significant interactions that are difficult to interpret within the theoretical framework guiding the research. Some of these interactions actually arise from the presence of…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
A high-dimensional $r$-factor model for an $n$-dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance matrix.…
In this article, we introduce a procedure for selecting variables in principal components analysis. The procedure was developed to identify a small subset of the original variables that best explain the principal components through…
We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
The design of experiments in psychology can often be summarized to participants reacting to stimuli. For such an experiment, the mixed effects model with crossed random effects is usually the appropriate tool to analyse the data because it…
Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…