Related papers: Estimation and Inference for Three-Dimensional Pan…
Within a supervised classification framework, labeled data are used to learn classifier parameters. Prior to that, it is generally required to perform dimensionality reduction via feature extraction. These preprocessing steps have motivated…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors,…
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are…
The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of…
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…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in…
Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…
Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
This work introduces a novel two-stage distributed framework to globally estimate constant parameters in a networked system, separating shared information from local estimation. The first stage uses dynamic average consensus to aggregate…
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,…
This article considers to model large-dimensional matrix time series by introducing a regression term to the matrix factor model. This is an extension of classic matrix factor model to incorporate the information of known factors or useful…
This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…