Related papers: Consistent estimation of high-dimensional factor m…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…
We propose a novel estimator for the principal component (PC) subspace tailored to the high-dimension, low-sample size (HDLSS) context. The method, termed Adaptive Reference-Guided (ARG) estimator, is designed for data exhibiting spiked…
Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how…
A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be…
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…
We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…
Hierarchical panel data models have recently garnered significant attention. This study contributes to the relevant literature by introducing a novel three-dimensional (3D) hierarchical panel data model, which integrates panel regression…
We propose a new method for statistical inference in generalized linear models. In the overparameterized regime, Principal Component Regression (PCR) reduces variance by projecting high-dimensional data to a low-dimensional principal…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…
Missing Not At Random (MNAR) values lead to significant biases in the data, since the probability of missingness depends on the unobserved values.They are ''not ignorable'' in the sense that they often require defining a model for the…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
We introduce a novel covariance estimator for portfolio selection that adapts to the non-stationary or persistent heteroskedastic environments of financial time series by employing exponentially weighted averages and nonlinearly shrinking…
Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
Principal Component Analysis (PCA) aims to find subspaces spanned by the so-called principal components that best represent the variance in the dataset. The deflation method is a popular meta-algorithm that sequentially finds individual…
In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…