On sparsity scales and covariance matrix transformations
成果类型：
Article
署名作者：
Battey, H. S.
署名单位：
Imperial College London
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asz014
发表日期：
2019
页码：
605617
关键词：
摘要：
We develop a theory of covariance and concentration matrix estimation on any given or estimated sparsity scale when the matrix dimension is larger than the sample size. Nonstandard sparsity scales are justified when such matrices are nuisance parameters, distinct from interest parameters, which should always have a direct subject-matter interpretation. The matrix logarithmic and inverse scales are studied as special cases, with the corollary that a constrained optimization-based approach is unnecessary for estimating a sparse concentration matrix. It is shown through simulations that for large unstructured covariance matrices, there can be appreciable advantages to estimating a sparse approximation to the log-transformed covariance matrix and converting the conclusions back to the scale of interest.