Monte Carlo cross validation

In order to choose correctly the dimension of calibration model in chemistry, a new simple and effective method named Ž . Monte Carlo cross validation MCCV is introduced in the present work. Unlike leave-one-out procedure commonly used in Ž . chemometrics for cross validation CV , the Monte Carlo cross validation developed in this paper is an asymptotically consistent method in determining the number of components in calibration model. It can avoid an unnecessary large model and therefore decreases the risk of over-fitting for the calibration model. The results obtained from simulation study showed that MCCV has an obviously larger probability than leave-one-out CV in choosing the correct number of components that the model should contain. The results from real data sets demonstrated that MCCV could successfully choose the appropriate model, but leave-one-out CV could not. q 2001 Elsevier Science B.V. All rights reserved.