ABSTRACT
To obtain asymptotic normality of the MLE, more restrictive conditions on f(x|θ) are needed. In particular, it will be assumed that (∂ 2/∂ θ 2)f(x|θ) exists and is continuous. This will rule out cases like the uniform distribution on the interval (0, θ ), θ > 0, where the maximum-likelihood estimate is the maximum of the sample, converges to the true value at the much faster rate of 1/n, and is not asymptotically normal. (See Example 2 of Section 14.)
