SiZer for smoothing splines

Smoothing splines are an attractive method for scatterplot smoothing. The SiZer approach to statistical inference is adapted to this smoothing method, named SiZerSS. This allows quick and sure inference as to which features in the smooth are really there as opposed to which are due to sampling artifacts, when using smoothing splines for data analysis. Applications of SiZerSS to mode, linearity, quadraticity and monotonicity tests axe illustrated using a real data example. Some small scale simulations are presented to demonstrate that the SiZerSS and the SiZerLL (the original local linear version of SiZer) often give similar performance in exploring data structure but they can not replace each other completely.