where ˜ f (y|x) is a predictive density estimator. See, for example,
the article by Lawless and Fredette (2005).
Remark 4. Note that the variances of the two normal approximations
are not close to that of the binomial distribution
B(n,p) when n is not large enough. It is mainly because the
mean mˆp is a random variable, but not a constant mp. Since
the mean of mˆp is mp, we still can use the Kullback–Leibler
distance between a predictive distribution and the binomial distribution
to evaluate the performance of the predictive distribution