Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models. Issue 5 (3rd September 2018)

• Record Type: Journal Article
• Authors: Bura, E.; Duarte, S.; Forzani, L.; Smucler, E.; Sued, M.
• Is Part Of: Statistics. Volume 52:Issue 5(2018)
• Page Start: 1005
• Page End: 1024
• Publication Date: 2018-09-03
• Subjects: M-estimation -- exponential family -- rank restriction -- non-convex -- parameter spaces; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1467420
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.