Local and Global Rank Tests for Multivariate Varying-Coefficient Models

Stephen G. Donald, Natércia Fortuna and Vladas Pipiras

Journal of Business & Economic Statistics, 2011, vol. 29, issue 2, 295-306

Abstract: In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions v ( X ) of some explanatory variables X and the coefficients in an unknown regression matrix θ ( Z ) depend on another set of explanatory variables Z . We provide statistical tests, called local and global rank tests, which allow one to estimate the rank of an unknown regression coefficient matrix θ ( Z ) locally at a fixed level of the variable Z or globally as the maximum rank over all levels of Z in a proper, compact subset of the support of Z , respectively. We apply our results to estimate the so-called local and global ranks in a demand system where budget shares are regressed on known functions of total expenditures and the coefficients in a regression matrix depend on prices faced by a consumer.

Date: 2011
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DOI: 10.1198/jbes.2010.07303

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