Improved Computation of the Standard Error in the Regression Coefficient Estimates of a Multivariate Calibration Model

A multivariate calibration model consists of regression coefficient estimates whose significance depends on the associated standard errors. A recently introduced leave-one-out (LOO) method for computing these standard errors is modified to achieve consistency with the jack-knife method. The proposed modification amounts to multiplying the LOO standard errors with the factor (n - 1)/n1/2, where n denotes the number of calibration samples. The potential improvement for realistic values of n is illustrated using a practical example.