A Cramér-Rao inequality for non differentiable models

We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\ér-Rao bound, although it does not require the differentiability of the model. Moreover, we show our efficiency bound to be always greater than the Cram\ér-Rao bound in smooth models, thus providing a sharper result.