CER Prediction Uncertainty
In this paper we compare the parametric bootstrap to the Delta method as tools for quantifying the uncertainty of predictions from a nonlinear cost-estimating relationship (CER) with a multiplicative error term. The bootstrap is a computationally-intensive resampling technique used to estimate bias and standard errors of statistical estimators. The validity of the bootstrap depends on asymptotic theory and is exact only in very large samples, whereas most CERs are estimated from small samples. The Delta method provides a linear approximation of the mean and variance for a nonlinear estimator. The Delta method also relies on asymptotic theory, but requires only a single computational pass through the data. We use Monte Carlo simulation to compare the two methods for quantifying the uncertainty of CER predictions based on a range of sample sizes.
Matthew S. Goldberg is Deputy Assistant Director for the National Security Division of the Congressional Budget Office (CBO). Prior to joining CBO in May 2004, Dr.
Goldberg was Director of the Cost and Acquisition Team at The CNA Corporation. He holds a bachelors degree in Economics/Mathematics from Queens College, CUNY; and a doctorate in Economics from the University of Chicago. He has been a defense analyst since 1980. He has also taught at UCLA, Georgetown, and George Mason Universities. His publications have appeared in such journals as Management Science, Naval Research Logistics, Technometrics, Journal of Econometrics, and The Engineering Economist. He was co-recipient of the 1997 Koopman Prize awarded by INFORMS for the best military application of operations research. He was co-recipient again in 2003 for the monograph Statistical Methods for Learning Curves and Cost Analysis.
Richard Seprling is a research analyst for the CNA Corpooration in Alexandria, VA. Before joining CNA full-time in October 2003, Dr. Sperling served as a consultant to CNA. Prior to that time, he was an economist for the U.S. Department of Agriculture. Dr. Sperling holds a bachelors degree in economics from the University of Illinois; and a doctorate in agricultural economics from Ohio State University, where he was awarded a USDA fellowship. His publications have appeared in the Journal of Agricultural Economics and the Stata Technical Bulletin.