What is the asymptotic behavior of Naïve Bayes under infinite data?

With infinite data, Naïve Bayes converges to stable parameter estimates, but not necessarily the true distribution.

As sample size increases, empirical estimates converge to expected values. However, due to independence assumption, NB may converge to a biased approximation of true distribution. Despite this, classification error may still approach Bayes optimal error under certain conditions.