Smoothing, splines and smoothing splines; their application in geomagnetism (Q1112537)

This paper is concerned with the application of spline smoothing in nonparametric regression on geomagnetic data. Some properties of well- known cubic smoothing splines and cubic least squares splines are discussed. It is asserted that in many important cases using smoothing splines is too expensive and least squares splines cannot model the data adequately. A penalized least squares cubic spline procedure is proposed that retains the computational efficiency of the least squares splines and overcomes its principal disadvantage. Effects of these splines are compared by treating them as variable-kernel smoothers. Applications are demonstrated by several numerical examples.