Related papers: Consistent estimation of high-dimensional factor m…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
A major concern when dealing with financial time series involving a wide variety ofmarket risk factors is the presence of anomalies. These induce a miscalibration of the models used toquantify and manage risk, resulting in potential…
In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
This work is devoted to the finite sample prediction risk analysis of a class of linear predictors of a response $Y\in \mathbb{R}$ from a high-dimensional random vector $X\in \mathbb{R}^p$ when $(X,Y)$ follows a latent factor regression…
Principal component analysis is a multivariate statistical method frequently used in science and engineering to reduce the dimension of a problem or extract the most significant features from a dataset. In this paper, using a similar notion…
Tensor time series data appears naturally in a lot of fields, including finance and economics. As a major dimension reduction tool, similar to its factor model counterpart, the idiosyncratic components of a tensor time series factor model…
We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the…
Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components…
We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
We propose a dynamic multiplicative factor model for process data, which arise from complex problem-solving items, an emerging testing mode in large-scale educational assessment. The proposed model can be viewed as an extension of the…
Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
While most of the convergence results in the literature on high dimensional covariance matrix are concerned about the accuracy of estimating the covariance matrix (and precision matrix), relatively less is known about the effect of…
Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weak…
This paper studies the estimation of characteristic-based quantile factor models where the factor loadings are unknown functions of observed individual characteristics while the idiosyncratic error terms are subject to conditional quantile…
We analyse the prediction error of principal component regression (PCR) and prove non-asymptotic upper bounds for the corresponding squared risk. Under mild assumptions, we show that PCR performs as well as the oracle method obtained by…