Can we define a best estimator in simple one-dimensional cases?

Éric Lantz (1) , François Vernotte (2)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 UTINAM - Univers, Transport, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213)

What is the best estimator for assessing a parameter of a probability distribution from a small number of measurements? Is the same answer valid for a location parameter like the mean as for a scale parameter like the variance? It is sometimes argued that it is better to use a biased estimator with low dispersion than an unbiased estimator with a higher dispersion. In which cases is this assertion correct? To answer these questions, we will compare, on a simple example, the determination of a location parameter and a scale parameter with three "optimal" estimators: the minimum-variance unbiased estimator, the minimum square error estimator, and the a posteriori mean.

Domaines: Optique / photonique; Optique [physics.optics]

Éric Lantz, François Vernotte. Can we define a best estimator in simple one-dimensional cases?. IEEE Signal Processing Magazine, 2013, 30, pp.151 - 156. ⟨10.1109/MSP.2013.2276532⟩. ⟨hal-00877479⟩