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

TL;DR

This note clarifies that the $hv$-block cross-validation method is not a BIBD, challenging previous assumptions about its theoretical properties and highlighting the need for further investigation into its consistency.

Contribution

The paper corrects a misconception about $hv$-block cross-validation, showing it is not a BIBD and thus its consistency remains unproven.

Findings

$hv$-block is not a BIBD.

Theoretical consistency of $hv$-block remains open.

Provides a Python program for counting sample occurrences.

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.