Discussion of "Estimating structured high- dimensional covariance and precision matrices: Optimal rates and adaptive estimation"

Professors Cai, Ren and Zhou ought to be congratulated for writing such a wonderful expository paper on optimal estimation of highdimensional covariance and precision matrices. Nearly all optimality results on large matrix estimation were established by the authors (and their coauthors). Thus, they are the most appropriate team to write this much needed review article. My discussion contains three sections.