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Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
Recent work by Ram\'irez et al. [2] has introduced Multi-Channel Factor Analysis (MFA) as an extension of factor analysis to multi-channel data that allows for latent factors common to all channels as well as factors specific to each…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units,…
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. We interpret the factorization in a new way and use it to generate missing attributes from test data. We provide a joint…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Factor Analysis based on multivariate $t$ distribution ($t$fa) is a useful robust tool for extracting common factors on heavy-tailed or contaminated data. However, $t$fa is only applicable to vector data. When $t$fa is applied to matrix…
We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial…
Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis…
Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their…
Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on the singular values of the lagged…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…
Factor analysis (FA) is a statistical tool for studying how observed variables with some mutual dependences can be expressed as functions of mutually independent unobserved factors, and it is widely applied throughout the psychological,…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…
Mixtures of factor analyzers (MFA) provide a powerful tool for modelling high-dimensional datasets. In recent years, several generalizations of MFA have been developed where the normality assumption of the factors and/or of the errors was…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
Confirmatory Factor Analysis (CFA) is a particular form of factor analysis, most commonly used in social research. In confirmatory factor analysis, the researcher first develops a hypothesis about what factors they believe are underlying…
Score Predictor Factor Analysis (SPFA) was introduced as a method that allows to compute factor score predictors that are -- under some conditions -- more highly correlated with the common factors resulting from factor analysis than the…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
The model implied by factor score predictors does not reproduce the non-diagonal elements of the observed covariance matrix as well as the factor loadings. It is therefore investigated whether it is possible to estimate factor loadings for…