We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix...

We revisit the twofold identification problem discussed by Cho, Ishida, and White (Neural Computation, 2011), which arises when testing for neglected nonlinearity by artificial neural networks. We do not use the so-called ¡°no-zero¡± condition and employ a sixth-order expansion to obtain the...

We provide mathematical proofs for the results in ¡°Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions¡± by Cho, Ishida, and White (2013).