Verifying the Solution from a Nonlinear Solver - A Case Study: Comment

摘要

In a recent article in this journal, B. D. McCullough and H. D. Vinod (2003; hereafter MV) argue that checking the condition number of the Hessian should be a standard part of checking the validity of any estimates obtained via nonlinear optimization. While we think that looking at the condition number of the Hessian is a good idea, we argue that the issue is not as straightforward as claimed by MV. To illustrate our point, we show that MV reached the wrong conclusion about the validity of the Ron Shachar and Barry Nalebuff (1999) solution. In Sections I-III of their article, MV note that it is possible for a well-coded log-likelihood program to declare convergence when some of the parameters are not identified for the given data set.