Related papers: Tests for principal eigenvalues and eigenvectors
We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Detecting structural changes in functional data is a prominent topic in statistical literature. However not all trends in the data are important in applications, but only those of large enough influence. In this paper we address the problem…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
This paper deals with analyzing structural breaks in the covariance operator of sequentially observed functional data. For this purpose, procedures are developed to segment an observed stretch of curves into periods for which second-order…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and…
We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly…
We study the long-standing problem of determining the number of principal components in econometric applications from a selective inference perspective. We consider i.i.d. observations from a $p$-dimensional random vector with $p<n$ and…
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…
Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…
We propose novel methods for change-point testing for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. We can detect general multiple structural changes in the tails of marginal…
This paper studies the identification of Structural Vector Autoregressions (SVARs) exploiting a break in the variances of the structural shocks. Point-identification for this class of models relies on an eigen-decomposition involving the…
This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to…
This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…