Bootstrap methods for a measurement estimation problem

In this paper, a new approach for the statistical characterization of a measurand is presented. A description of how different bootstrap techniques can be applied in practice to estimate successfully a measurand probability density function (pdf) is given. When the direct observation of a quantity of interest is practically impossible such as in nondestructive testing, it is necessary to estimate such quantity, which is also called measurand. The statistical characterization of any estimator is important, because all the uncertainty features can be accessible to qualify such estimator. On the other hand, most of the time, the large-scale repetition of an experiment is not economically feasible, so that the Monte Carlo methods cannot be used directly for uncertainty characterization. Bootstrap methods have proved to be a potentially useful alternative. Moreover, a biased bootstrap recent technique, with which robust parameter estimates are obtained, is used. This technique is extended to be used in measurand estimation. An extended nested bootstrap improvement for the measurand pdf estimation is also presented. These techniques are applied to a realistic multidimensional measurand-estimation problem of groove dimensioning using remote field eddy current inspection. Measurand uncertainty characterization using the bootstrap techniques generally gives an accurate pdf estimation