A linear algebra approach to HP-splines frequency parameter selection

In this work we propose a strategy to select the frequency parameter of hyperpolic-polynomial P-splines, HP-splines for shortness. HP-splines are hyperpolic-polynomial penalized splines where polynomials are replaced by the richer class of exponential-polynomials and a tailored discrete penalty term is used. HP-splines reduce to P-splines when setting the frequency parameter to zero but are more suitable to data with an exponential trend, which are frequently encountered in applications. Yet, they require an effective strategy to select the frequency parameter in addition to the one needed for selecting the smoothing parameter. Here, we propose a strategy that involves a linear algebra approach for Tikhonov regularization problems adapted to HP-splines. As shown in the numerical experiments, our strategy provides an efficient criterion yielding to HP-splines that better capture the trend suggested by the fitted data.