Abstract: In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in highdimension and that does not require imputation of the missing data. We establish non-asymptotic sparsity oracle inequalities for the estimation of the covariance matrix with the Frobenius and spectral norms, valid for any setting of the sample size and the dimension of the observations. We further establish minimax lower bounds showing that our rates are minimax optimal up to a logarithmic factor.
The focus of REF is on estimation of approximately low rank covariance matrices with a matrix version of the lasso algorithm.
High-dimensional covariance matrix estimation with missing observations
arXiv: Statistics Theory
Mathematics