# A uniform bound on the operator norm of sub-Gaussian random matrices and its applications

Grigory Franguridi, Hyungsik Roger Moon

Research output: Contribution to journalArticlepeer-review

## Abstract

For an N × T random matrix X(β) with weakly dependent uniformly sub-Gaussian entries xit(β) that may depend on a possibly infinite-dimensional parameter β ∈ B, we obtain a uniform bound on its operator norm of the form E supβB ||X(β)|| ≤ CK (√max(N,T) + γ2(B,dB)), where C is an absolute constant, K controls the tail behavior of (the increments of) xit(·), and γ2(B,dB) is Talagrand's functional, a measure of multiscale complexity of the metric space (B,dB). We illustrate how this result may be used for estimation that seeks to minimize the operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data.

Original language English Econometric Theory https://doi.org/10.1017/S0266466621000177 Accepted/In press - 2021