A Note on the Problem of Statistical Calibration

The well-known problem of obtaining a satisfactory predictor of a variable X from another variable Y, where X and Yhave a joint probability distribution, is reconsidered. The data available are the pairs of observations (xi,yi), i = 1,...,n, of a calibration experiment in which only the bivariate random variables (X, Y) can be observed. A new predictor is proposed and is claimed to have advantages over the Inverse Predictor that has been advocated by various authors in this case. A practical example is provided to facilitate a comparison of various predictors, and to demonstrate that the new predictor is appropriate for many practical cases notably of small sample sizes. This new predictor is useful not only for the normal case, but also when the conditional distribution of Ygiven X = xo is a member of the non-normal location and scale family and/or in some cases when the error variances show heteroscedasticity.