The Statistical Properties of the Equity Estimator: A Reply

Abstract

Hill and Cartwright examined the relative performance of ordinary least squares, the Equity estimator, and the Stein estimator on four scanner data sets. Based on this limited simulation, they claimed that the Stein estimator is an attractive alternative to the Equity estimator. In this reply, we demonstrate that their conclusions are not well founded and that a more comprehensive evaluation indicates that the Equity estimator dominates the Stein estimator in wide regions of the parameter space.

KEY WORDS:

• Biased estimators
• Monte Carlo simulation