Who's Afraid of Reduced-Rank Parameterizations of Multivariate Models? Theory and Example

Scott Gilbert and Petr Zemcik ()

CERGE-EI Working Papers from The Center for Economic Research and Graduate Education - Economics Institute, Prague

Abstract: Reduced-rank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and non-Gaussian (GLM, GAM, etc.) multivariate models, the present work gives a unified, explicit theory for the general asymptotic (normal) distribution of maximum likelihood estimators (MLE). MLE can be complex and computationally difficult, but we show a strong asymptotic equivalence between MLE and a relatively simple minimum (Mahalanobis) distance estimator. The latter method yields particularly simple tests of rank, and we describe its asymptotic behavior in detail. We also examine the method's performance in simulation and via analytical and empirical examples.

Keywords: Conditional median; Conditional standard deviation; Multivariate coefficient matrix; Reduced-rank estimation test; Asymptotic theory (search for similar items in EconPapers)
JEL-codes: C13 C15 C30 (search for similar items in EconPapers)
Date: 2004-05
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Who's afraid of reduced-rank parameterizations of multivariate models? Theory and example (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:cer:papers:wp223

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