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多元变系数模型的局部与全局秩检验AI 解读

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…

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对称矩阵的秩估计：不定矩阵估计量情形AI 解读

In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently and to have either a Kronecker product or an arbitrary structure. These assumptions are standard although they exclude the case when the matrix estimator is positive or negative semidefinite. We adapt and reexamine here some available rank…