Simple formulae for bias and mean square error computation [DSP tips and tricks]

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

49 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number6530724
Pages (from-to)162-165
Journal / PublicationIEEE Signal Processing Magazine
Volume30
Issue number4
Online published12 Jun 2013
Publication statusPublished - Jul 2013

Abstract

In any estimation problem, there is always a need to find the bias and mean square error (MSE) of an estimator. These values are then compared against their sample averages obtained from simulation to confirm the theoretical development, and/or the Cram?r-Rao lower bound (CRLB) [1] to assess the optimality of the estimator. When the estimator is a nonlinear function of the measurements, it is rather difficult to derive exact expressions for the bias and MSE. Based on Taylor series expansion (TSE) of the estimator cost function near the true value, [2] provides a generic approximation for these performance measures. In [3], equations for bias and variance are obtained by a direct TSE of the estimator function. Their difference is that [2] is a TSE of the estimator cost function, while [3] is a TSE of the estimator itself. We shall review the bias and MSE formulas obtained from these two approaches, provide several representative application examples, and compare their results. It will be explained that for linear parameter estimation problems, both techniques give identical and exact bias and MSE expressions. However, the former has a wider applicability over the latter for nonlinear estimation, particularly when the estimate is not an explicit function of the measurements. © 1991-2012 IEEE.

Citation Format(s)

Simple formulae for bias and mean square error computation [DSP tips and tricks]. / So, Hing Cheung; Chan, Yiu Tong; Ho, K. C. et al.
In: IEEE Signal Processing Magazine, Vol. 30, No. 4, 6530724, 07.2013, p. 162-165.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review