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 are 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. Marron’s research was supported by the Dept. of Stat. and Appl. Prob., National Univ. of Singapore, and by the National Science Foundation Grant DMS-9971649. Zhang’s research was supported by the National Univ. of Singapore Academic Research grant R-155-000-023-112. The Editor, the Associate Editor, and the referees are appreciated for their invaluable comments and suggestions that help improve the article significantly.