A study of the effect of measurement error in predictor variables in nondestructive assay

It is not widely known that ordinary least squares estimates exhibit bias if there are errors in the predictor variables. For example, enrichment measurements are often fit to two predictors: Poisson-distributed count rates in the region of interest and in the background. Both count rates have at least random variation due to counting statistics. Therefore, the parameter estimates will be biased. In this case, the effect of bias is a minor issue because there is almost no interest in the parameters themselves. Instead, the parameters will be used to convert count rates into estimated enrichment. In other cases, this bias source is potentially more important. For example, in tomographic gamma scanning, there is an emission stage which depends on predictors (the “system matrix”) that are estimated with error during the transmission stage. In this paper, we (1) provide background information for the impact and treatment of errors in predictors, (2) present results of candidate methods of compensating for the effect, (3) review some of the nondestructive assay situations where errors in predictors occurs, and (4) provide guidance for when errors in predictors should be considered in nondestructive assay.