$hv$-Block Cross Validation is not a BIBD: a Note on the Paper by Jeff Racine (2000)

Abstract

This note corrects a mistake in the paper "consistent cross-validatory model-selection for dependent data: $hv$-block cross-validation" by Racine (2000). In his paper, he implied that the therein proposed $hv$-block cross-validation is consistent in the sense of Shao (1993). To get this intuition, he relied on the speculation that $hv$-block is a balanced incomplete block design (BIBD). This note demonstrates that this is not the case, and thus the theoretical consistency of $hv$-block remains an open question. In addition, I also provide a Python program counting the number of occurrences of each sample and each pair of samples.