Projection pursuit in high dimensions.

ABSTRACT: Projection pursuit is a classical exploratory data analysis method to detect interesting low-dimensional structures in multivariate data. Originally, projection pursuit was applied mostly to data of moderately low dimension. Motivated by contemporary applications, we here study its properties in high-dimensional settings. Specifically, we analyze the asymptotic properties of projection pursuit on structureless multivariate Gaussian data with an identity covariance, as both dimension p and sample size n tend to infinity, with [Formula: see text] Our main results are that (i) if [Formula: see text] then there exist projections whose corresponding empirical cumulative distribution function can approximate any arbitrary distribution; and (ii) if [Formula: see text], not all limit

SUBMITTER: Bickel PJ 

PROVIDER: S-EPMC6140545 | biostudies-literature | 2018 Sep

REPOSITORIES: biostudies-literature