Testing the Rank and Definiteness of Estimated Matrices With Applications to Factor, State-Space and ARMA Models
本文提出一种基于高斯消去LDU分解的检验方法，用于检验任意一致渐近正态估计矩阵的秩和半正定性，可应用于识别结构模型、确定状态空间模型变量数、ARMA模型阶数以及因子分析中的因子数量。
Abstract Consider any consistent, asymptotically normal estimate ǎ of an arbitrary rectangular or square matrix A. This article derives an explicit test for the rank of A and a related test of (semi) definiteness of A. Potential applications include testing for identification of structural models, testing for the number of state variables in state-space models (including tests for the order of autoregressive moving average (ARMA) processes), consumer demand analysis applications, and testing for the number of factors in factor analysis and related procedures. The test is based on the Gaussian elimination Lower-Diagonal-Upper triangular (LDU) decomposition. The test is illustrated with an empirical application to testing the order of ARMA processes.