Penalized hyperbolic-polynomial splines

With the aim of generalizing P-splines, we here define a special type penalized splines, called HP-splines, where polynomial splines are replaced by richer class hyperbolic-polynomial and suitably tailored discrete penalty term is used. Hyperbolic-polynomial important in several applications, natural generalization consisting piecewise-defined functions with segments spanned ‘atoms’ x r e ? = 0 , … ? ? R . that reduce to P-splines for more suitable data an exponential trend which frequent applications.