The estimation of large covariance and precision matrices is fundamental in modern
multivariate analysis. However, problems arise from the statistical analysis of large panel …

Functional data analysis (FDA) involves the analysis of data whose ideal units of
observation are functions defined on some continuous domain, and the observed data …

The paper deals with the estimation of a high dimensional covariance with a conditional
sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance …

This package includes both Mathematical Statistics: Basic Ideas and Selected Topics,
Volume I, Second Edition, as well as Mathematical Statistics: Basic Ideas and Selected …

Principal component analysis (PCA) is a widely used technique for dimension reduction,
data processing, and feature extraction. The three tasks are particularly useful and important …

Sparse PCA: Optimal rates and adaptive estimation Page 1 The Annals of Statistics 2013, Vol.
41, No. 6, 3074–3110 DOI: 10.1214/13-AOS1178 © Institute of Mathematical Statistics, 2013 …

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts
latent principal factors that contribute to the most variation of the data. When data are stored …

This paper considers the sparse eigenvalue problem, which is to extract dominant (largest)
sparse eigenvectors with at most k non-zero components. We propose a simple yet effective …

This is an expository paper that reviews recent developments on optimal estimation of
structured high-dimensional covariance and precision matrices. Minimax rates of …

We perform a finite sample analysis of the detection levels for sparse principal components
of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse …