Related papers: Tests for principal eigenvalues and eigenvectors

This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…

In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…

Explicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic analysis of the hypergeometric functions…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

Factor analysis is a statistical technique employed to evaluate how observed variables correlate through common factors and unique variables. While it is often used to analyze price movement in the unstable stock market, it does not always…

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of…

We examine hypothesis testing within a principal-agent framework, where a strategic agent, holding private beliefs about the effectiveness of a product, submits data to a principal who decides on approval. The principal employs a hypothesis…

This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of…

Hyperparameters play a critical role in machine learning. Hyperparameter tuning can make the difference between state-of-the-art and poor prediction performance for any algorithm, but it is particularly challenging for structure learning…

How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite…

We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…

Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…

This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of…

Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that a single factor is…

We derive bounds on the eigenvalues of saddle-point matrices with singular leading blocks. The technique of proof is based on augmentation. Our bounds depend on the principal angles between the ranges or kernels of the matrix blocks.…

We propose a sequential monitoring scheme to find structural breaks in real estate markets. The changes in the real estate prices are modeled by a combination of linear and autoregressive terms. The monitoring scheme is based on a detector…