Some Details of Nonlinear Estimation

The traditional view adopted by statistics and econometrics texts is that, in order to solve a nonlinear least squares (NLS) or nonlinear maximum likelihood (NML) problem, a researcher need only use a computer program. This point of view maintains two implicit assumptions: (1) one program is as good as another; and (2) the output from a computer is reliable. Both of these maintained assumptions are false. Recently the National Institute of Standards and Technology (NIST) released the “Statistical Reference Datasets” (StRD), a collection of numerical accuracy benchmarks for statistical software. It has four suites of tests: univariate summary statistics, one-way analysis of variance, linear regression, and nonlinear least squares. Within each suite the problems are graded according to level of difficulty: low, average, and high. NIST provides certified answers to fifteen digits for linear problems, and eleven digits for nonlinear problems. Complete details can be found at http://www.nist.gov/itl/div898/strd. Nonlinear problems require starting values, and all the StRD nonlinear problems come with two sets of starting values. Start I is far from the solution and makes the problem hard to solve. Start II is near to the solution and makes the problem easy to solve. Since the purpose of benchmark testing is to say something useful about