ABSTRACT
In the previous chapter we studied the almost sure convergence of various types of maximum estimators. We found that smoothness (that is, several times differentiability) of the criterion function h(s,θ) has nothing to do with consistency of maximum estimators. However, if we want to establish asymptotic normality of maximum estimators, then some sort of stochastic differentiability seems to be necessary. In this chapter, I shall introduce a concept of twice stochastic differentiability, which is based on an idea of D. Pollard (see Reference [8] to this chapter) and which serves our purpose. The concept is very similar to the concept of ordinary twice differentiability [see (P.9.12+13)] where we just replace the ordinary second order remainder term by a stochastic remainder term.
