Squared-norm empirical processes

Publication date: Available online 10 March 2019Source: Statistics & Probability LettersAuthor(s): Vincent Q. Vu, Jing LeiAbstractThis note extends a result of Mendelson on the supremum of a quadratic process to squared norms of functions taking values in a Banach space. Our method of proof is a reduction by a symmetrization argument and simple observation about the additivity of the generic chaining functional. We demonstrate an application to positive linear functionals of the sample covariance matrix and the apparent variance explained by principal components analysis (PCA).

Source: Statistics and Probability Letters - March 11, 2019 Category: Statistics Source Type: research