$hv$-Block Cross Validation is not a BIBD: a Note on the Paper by Jeff Racine (2000)
It addresses a theoretical flaw in a method for model selection with dependent data, but is incremental as it only corrects an error without proposing new solutions.
This note corrects a mistake in a 2000 paper by Racine, showing that $hv$-block cross-validation is not a balanced incomplete block design, which undermines the claimed theoretical consistency for dependent data.
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.