This dissertation develops a uni ed framework to study the (asymptotic) properties of all (periodic) spline based estimators, that is of regression, penalized and smoothing splines. The explicit form of the periodic Demmler-Reinsch basis of general degree in terms of exponential splines allows to derive the exact expression for the equivalent kernel of all spline estimators simultaneously. The corresponding bandwidth, which
drives the asymptotic behavior of spline estimators, is shown to be a function of both
the number of knots and the smoothing parameter. A strategy for the optimal bandwidth selection is discussed.
