There are two popular smoothing parameter selection methods for spline smoothing. First, criteria that approximate the average mean squared error of the estimator (e.g. generalized cross validation) are widely used. Alternatively, the maximum likelihood paradigm can be employed under the...

In this paper we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (i) as a standard (fixed effect) nonparametric model, (ii) using the mixed model framework with the spline coefficients as random effects...

This article develops a unified framework to study the (asymptotic) properties of (periodic) spline based estimators, that is of regression, penalized and smoothing splines. We obtain an explicit form of the Demmler-Reinsch basis of general degree in terms of exponential splines and...

We present a nonparametric method to decompose a times series into trend, seasonal and remainder components. This fully data-driven technique is based on penalized splines and makes an explicit characterization of the varying seasonality and the correlation in the remainder. The procedure takes...