MSE < Variance? A pitfall in calculating the mean square error

Article type: Research Article

Authors: Ng, Edmond Siu-Woon

Affiliations: Department of Health Services Research and Policy, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH, UK. E-mail: edmond.ng@lshtm.ac.uk

Abstract: When calculating the mean square error (MSE), it is possible to encounter a situation where the variance of a parameter of interest is larger than its mean square error. In theory, this is impossible because MSE is the sum of variance and bias squared; even when bias is zero, the MSE should be equal to, and not less than, the variance. This short note explains why this is indeed an error with a mathematical proof, demonstrates how this could happen using a small simulation study, and shows how to avoid making such an error in the derivation of the MSE.

Keywords: Mean square error, variance, bias, simulation studies

DOI: 10.3233/MAS-2011-0195

Journal: Model Assisted Statistics and Applications, vol. 6, no. 4, pp. 369-371, 2011