Tag Archives: restricted cubic splines

Restricted cubic splines in regression

Earlier this year, Angela O’Brien-Malone and I were working on some research that involved quantile regression using restricted cubic splines. Almost without exception, the papers that I read on cubic splines cited a paper by Stone and Koo published in 1985 in the Statistical Computing Section of the Proceedings of the American Statistical Association. Clearly, the authors of the papers that I read had better library resources than I, or perhaps they did not actually read the original paper and merely cited secondary sources! Despite contacting several libraries, I found myself completely unable to obtain a copy of the paper.

Eventually I had the idea of looking to see whether I could contact the authors and by good fortune found the email address for Charles J. Stone, Professor Emeritus of Statistics at the University of California (Berkley). By even greater fortune, Professor Stone had a copy of the paper which he kindly scanned and emailed to me. Now I, like many other readers of mathematics, like to see it beautifully typeset but in 1985 when Stone and Koo’s paper was originally published, the Statistical Computing Section of the ASA was using fonts that did the mathematics little justice. So, with Professor Stone’s permission, and as a way of saying “thank you”, I have reprintted the paper using LaTex. The images are taken directly from a scanned copy of the original.

Two versions of the paper are available for download here: For North American readers, there is a copy fitted to letter-size paper. For others, there is an A4 sized copy. The paper should be cited as:
Stone, C. J., & Koo, C.-Y. (Cha-Yong) (1985). Additive splines in statistics. Proceedings of the Statistical Computing Section, American Statistical Association 27, 45-48.

I should add that I have been very remiss in taking so long to make the paper available. I shall post an excuse at a later date …