Testing with Cubic Smoothing Splines

In this paper, we present some possible ways to perform estimation and testing for cubic smoothing splines. Special emphasis is placed on the analysis of correlated data, when using semi-parametric regression models (Schimek, 2000), and the so-called spline growth model (Nummi and Koskela, 2008; Nummi et al., 2017), an extension of the basic growth curve model (Potthoff and Roy, 1964; Rao, 1965). Furthermore, practical applications in fields such as medicine and animal breeding are introduced, highlighting the versatility and efficacy of cubic smoothing splines in real-world applications.