This user guide presents a popular smoothing tool with practical applications in machine learning, engineering, and statistics.

Paul H. C. Eilers is Professor Emeritus of Genetical Statistics at the Erasmus University Medical Center Rotterdam. He received his Ph.D. in biostatistics. His research interests include high-throughput genomic data analysis, chemometrics, smoothing, longitudinal data analysis, survival analysis, and statistical computing. He has published extensively on these subjects.

1. Introduction; 2. Bases, penalties, and likelihoods; 3. Optimal smoothing in action; 4. Multidimensional smoothing; 5. Smoothing of scale and shape; 6. Complex counts and composite links; 7. Signal regression; 8. Special subjects; A. P-splines for the impatient; B. P-splines and competitors; C. Computational details; D. Array algorithms; E. Mixed model equations; F. Standard errors in detail; G. The website.