No free lunch with the sandwich [sandwich estimator]

In nonlinear regression theory, the sandwich estimator of the covariance matrix of the model parameters is known as a consistent estimator, even when the parameterized model does not contain the regression. However, in the latter case, we emphasize the fact that the consistency of the sandwich holds only if the inputs of the training set are the values of independent identically distributed random variables. Thus, in the frequent practical modeling situation involving a training set whose inputs are deliberately chosen and imposed by the designer, we question the opportunity to use the sandwich estimator rather than the simple estimator based on the inverse squared Jacobian.