L1-Optimal Splines for Outlier Rejection

In this article, we consider control theoretic splines with L optimization for rejecting outliers in data. Control theoretic splines are either interpolating or smoothing splines, depending on a cost function with a constraint defined by linear differential equations. Control theoretic splines are effective for Gaussian noise in data since the estimation is based on L optimization. However, in practice, there may be outliers in data, which may occur with vanishingly small probability under the Gaussian assumption of noise, to which L-optimized spline regression may be very sensitive. To achieve robustness against outliers, we propose to use L optimality, which is also used in support vector regression. A numerical example shows the effectiveness of the proposed method.