Smoothing Spline Growth Curves With Covariates
Abstract
We adapt the interactive spline model of Wahba to growth curves with covariates. The smoothing spline formulation permits a nonparametric representation of the growth curves. In the limit when the discretization error is small relative to the estimation error, the resulting growth curve estimates often depend only weakly on the number and locations of the knots. The smoothness parameter is determined from the data by minimizing an empirical estimate of the expected error. We show that the risk estimate of Craven and Wahba is a weighted goodness of fit estimate. A modified loss estimate is given, where $\sigma^2$ is replaced by its unbiased estimate.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.05087
 Bibcode:
 2018arXiv180305087R
 Keywords:

 Statistics  Methodology;
 Mathematics  Statistics Theory;
 Physics  Data Analysis;
 Statistics and Probability;
 Physics  Plasma Physics
 EPrint:
 Comm. in Statistics 22, pp. 17951818 (1993)