Why always seek the expected value? A discussion relating to the Lp norm

The process of estimating a measurand is based on the choice of an appropriate estimator. The metrologist usually makes this choice by comparing estimator properties such as unbiasedness, efficiency and robustness. We show that when dealing with asymmetric parent distributions, the expected value might not correspond to the measurand value; hence it might not be the correct parameter to estimate. In such cases, another location parameter can fit the measurand better and the properties of candidate estimators should be assessed in relation to such parameters. The paper discusses two examples with reference to the class of the L-p parameters and estimators, which include several commonly used in metrology.