  We consider the weighted least squares spline approximation of a noisy
dataset. By interpreting the weights as a probability distribution, we maximize
the associated entropy subject to the constraint that the mean squared error is
prescribed to a desired (small) value. Acting on this error yields a robust
regression method that automatically detects and removes outliers from the data
during the fitting procedure, by assigning them a very small weight. We discuss
the use of both spline functions and spline curves. A number of numerical
illustrations have been included to disclose the potentialities of the
maximal-entropy approach in different application fields.
