Spline smoothing for experimental data under zero median of the noise

We propose an algorithm for computing parameter estimates for a smoothing cubic spline that minimize the estimated expectation of losses. Instead of the usual assumption that the noise is centered we use an assumption which is more realistic for many practical smoothing problems, namely that it is zero median. The problem setting is augmented by prior deterministic information in the form of constraints on linear combinations of parameters of spline functions. We obtain explicit representations of such estimates and give their qualitative interpretation. Based on the results of a numerical experiment, we establish a high degree of robustness of the solutions to the presence of outliers in the measurements, including same sign outliers, and the possibility to fairly reliably determine the actual accuracy of the resulting estimates of spline parameters by the attained minimum risk value.