English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For an  			 		 $N \times T$ 		random matrix  			 		 $X(\beta )$ 		with weakly dependent uniformly sub-Gaussian entries  			 		 $x_{it}(\beta )$ 		that may depend on a possibly infinite-dimensional parameter  			 		 $\beta \in \mathbf {B}$ 		, we obtain a uniform bound on its operator norm of the form  			 		 $\mathbb {E} \sup _{\beta \in \mathbf {B}} ||X(\beta )|| \leq CK \left (\sqrt {\max (N,T)} + \gamma _2(\mathbf {B},d_{\mathbf {B}})\right )$ 		, where  C  is an absolute constant,  K  controls the tail behavior of (the increments of)  			 		 $x_{it}(\cdot )$ 		, and  			 		 $\gamma _2(\mathbf {B},d_{\mathbf {B}})$ 		is Talagrand’s functional, a measure of multiscale complexity of the metric space  			 		 $(\mathbf {B},d_{\mathbf {B}})$ 		. 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.

A UNIFORM BOUND ON THE OPERATOR NORM OF SUB-GAUSSIAN RANDOM MATRICES AND ITS APPLICATIONS