Local and Global Rank Tests for Multivariate Varying-Coefficient Models
针对多元变系数模型，提出局部与全局秩检验，用于估计回归系数矩阵的秩，并应用于需求系统中预算份额对总支出的回归分析。
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.