A minimax approach to combining means, with practical examples

Abstract Eberhardt, K.R., Reeve, C.P. and Spiegelman, C.H., 1989. A minimax approach to combining means, with practical examples. Chemometrics and Intelligent Laboratory Systems , 5: 129–148. This paper describes a method for combining sample means that accounts for bias in those means. It compares the unweighted mean, the weighted mean using reciprocal estimated variances for weights, and a minimax weighted mean. When the individual means are subject to nontrivial biases we show that the minimax estimator can lead to important decreases in mean squared error and confidence interval width. Our recommendations are based on statistical theory and on simulations based on three Standard Reference Material data sets.