Laplace's method and BIC model selection for least absolute value criterion.

In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in l o g (n) remains the same in the context of a selection of explanatory variables by least absolute value regression. [ABSTRACT FROM AUTHOR]