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).

This book is intended to provide a somewhat more comprehensive and unified treatment of large sample theory than has been available previously and to relate the fundamental tools of asymptotic theory directly to many of the estimators of interest to econometricians. In addition, because economic...