GROW e-variable.md

created	2024-08-29
lastmod	2024-09-02

Stands for "Growth rate optimality in worst case."

Similar to [[REGROW e-variable]] in that it seeks to extend [[GRO e-variable]] to composite alternatives, but we do not compare to the GRO process. Instead, we simply look for the process $(M_t)$ maximizing $$ \inf_{Q\in\calQ} \E_Q \log M_\tau. $$ Both REGROW and GROW should be considered as methods to extend the GRO condition to composite alternatives.

GROW can be found by minimizing [[KL divergence]] between the convex hull of null and alternative distributions. The likelihood ratio that achieves this minimum is an [[e-value]].