Model selection through a statistical analysis of the minimum of a weighted least squares cost function

Combining (i) a statistical interpretation of the minimum of a Weighted Least Squares cost function and (ii) the principle of parsimony, a model selection strategy is proposed. First, it is compared via simulation to model selection methods based on information criteria (AIC and MDL type). The first kind of simulations shows that the cost function approach outperforms in selecting the true model, especially when the number of data is very small compared with the number of parameters to be estimated. Next, the model metaselection proposed by de Luna and Skouras [X. De Luna, K. Skouras, Choosing a model selection strategy, Scand. J. Stat. 30(1) (2003) 113–128.] is employed as an objective method to choose the best model selection method. Applied to one of their examples, clearly the cost function strategy is selected as the best method. Finally, on a set of field data, the cost function approach is used for selecting the relevant parameters of a complex model.