# Who invented k-fold cross-validation?

I am looking for a reference to the paper where k-fold cross-validation was introduced (rather than just a good academic reference for the subject). Perhaps it is too far back in the mists of time to unambiguously identify the very first paper, so any early papers where the idea was used would be of interest.

The earliest I am aware of are

P. A. Lachenbruch and M. R. Mickey, “Estimation of error rates in discriminant analysis,” Technometrics, vol. 10, no. 1, pp. 1–12, Feb. 1968.

and

A. Luntz and V. Brailovsky, “On estimation of characters obtained in statistical procedure of recognition (in Russian),” Techicheskaya Kibernetica, vol. 3, 1969.

but as far as I can tell they only cover leave-one-out cross-validation (my technical Russian isn't all it could be ;o).

• I assume you're familiar with Stigler's law? (To be interpreted a bit more broadly than as stated.) :) Apr 18, 2012 at 20:34
• I learn something new every day! An early reference will do if the original inventor is unknown. I suspect it is one of those things that has been invented independently multiple times, but the history is interesting. Apr 19, 2012 at 12:12

One paper that might be worth consulting is

Stone M. Cross-validatory choice and assessment of statistical predictions. J. Royal Stat. Soc., 36(2), 111–147, 1974.

I have seen references to

Mosteller F. and Tukey J.W. Data analysis, including statistics. In Handbook of Social Psychology. Addison-Wesley, Reading, MA, 1968.

as an early clear description of $k$-fold cross-validation, but I don't have this manuscript.

The 1931 paper

Larson S. The shrinkage of the coefficient of multiple correlation. J. Educat. Psychol., 22:45–55,1931.

is mentioned, e.g. by Stone, as an early example where a randomly selected validation set is put aside for later assessment of the model.

• The Mosteller and Tukey reference looks a good start +1 (I presume it is Tukey rather than Turkey! ;o) Apr 19, 2012 at 12:11
• @DikranMarsupial, Ha, apologies to Tukey. I copy-pasted the reference and I didn't notice the misspelled name. Yes it is definitely Tukey.
– NRH
Apr 19, 2012 at 12:48
• Mosteller and Tukey: books.google.pl/… Mar 23, 2016 at 21:05