(eng): In continuous parametrized models with i.i.d. observations we consider finite quantizations. We study asymptotic properties of the estimators minimizing disparity between the observed and expected frequencies in the quantization cells, and asymptotic properties of the goodnes of fit tests rejecting the hypotheses when the disparity is large. We show that the inefficiency of the estimators and tests can be measured by the decrease of the Fisher information due to quantization.