On the Choice of Regression in Linear Calibration. Comments on a paper by R. G. Krutchkoff

In a paper by R. G. Krutchkoff, “Classical and Inverse Regression Methods of Calibration,” two methods of Calibration are compared by means of the Monte Carlo technique. He comes to the conclusion that the inverse approach to the Calibration problem has a uniformly smaller mean square error than the classical approach. Our theoretical treatment of the problem shows that the conclusion is true only for small samples. It is shown that when more than one observation is made on y the advantage of the inverse approach is reduced. A large sample formula for the ratio of the two mean square errors is derived which mainly conforms to the result by Krutchkoff.