What are the theoretical guarantees of Naïve Bayes consistency?

Naïve Bayes is consistent under correct model specification and sufficient data.

A classifier is consistent if it converges to the Bayes optimal classifier as sample size increases. Naïve Bayes is consistent when independence assumptions hold and parameter estimates converge to true distributions. Under misspecification, it may still be asymptotically optimal in terms of classification error rather than probability accuracy.