Inducement of population sparsity

Abstract

AbstractThe pioneering work on parameter orthogonalization by Cox and Reid is presented as an inducement of abstract population‐level sparsity. This is taken as a unifying theme for this article, in which sparsity‐inducing parameterizations or data transformations are sought. Three recent examples are framed in this light: sparse parameterizations of covariance models, the construction of factorizable transformations for the elimination of nuisance parameters, and inference in high‐dimensional regression. Strategies for the problem of exact or approximate sparsity inducement appear to be context‐specific and may entail, for instance, solving one or more partial differential equations or specifying a parameterized path through transformation or parameterization space. Open problems are emphasized.