The traditional M test requires a consistent estimation of the asymptotic variancecovariance matrix of the estimated moments (the AVC matrix). By extending the approach of Kiefer, Vogelsang, and Bunzel (KVB; 2000, Econometrica), Kuan and Lee (KL; 2006, Journal of the American Statistical Association) contributed a new type of M test without the AVC matrix estimation but with recursive model est...

This theory provides a compact formulation of Gauss-Jordan elimination for matrices represented as functions. Its distinctive feature is succinctness. It is not meant for large computations. 1 Gauss-Jordan elimination algorithm theory Gauss-Jordan-Elim-Fun imports Main begin Matrices are functions: type-synonym ′a matrix = nat ⇒ nat ⇒ ′a In order to restrict to finite matrices, a matrix is usua...

The 0− 1 matrix A contains a 0− 1 matrix M if some submatrix of A can be transformed into M by changing some ones to zeroes. If A does not contain M , then A avoids M . Let ex(n,M) be the maximum number of ones in an n×n 0−1 matrix that avoids M , and let exk(m,M) be the maximum number of columns in a 0− 1 matrix with m rows that avoids M and has at least k ones in every column. A method for bo...

It is pointed out that the phase convention of the CKM matrix V aaects texture analysis of the quark mass matrices (M u ; M d) when we try to describe (M u ; M d) by the observable quantities (quark masses and CKM matrix parameters) only. This is demonstrated for a case of the non-Hermitian Fritzsch-type mass matrix (f M u ; f M d), which is a general expression of quark mass matrix (M u ; M d)...