Related papers: The High-Dimensional Asymptotics of Principal Comp…

We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first main result shows that PCR performs comparably to the oracle…

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…

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…

We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…

In this paper, we investigate the impact of high-dimensional Principal Component (PC) adjustments on inferring the effects of variables on outcomes, with a focus on applications in genetic association studies where PC adjustment is commonly…

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

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 regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…

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…

With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on…

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…

We introduce Adaptive Subspace PCA (AS-PCA), a framework for principal component analysis of random elements in a general separable Hilbert space. AS-PCA projects the covariance operator onto a data-adaptive finite-dimensional subspace…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

A common feature of high-dimensional data is that the data dimension is high, however, the sample size is relatively low. We call such data HDLSS data. In this paper, we study asymptotic properties of the first principal component in the…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…

We analyze principal component regression (PCR) in a high-dimensional error-in-variables setting with fixed design. Under suitable conditions, we show that PCR consistently identifies the unique model with minimum $\ell_2$-norm. These…

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This…

Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be…