Consistency and Asymptotic Normality for Estimating Functions

Abstract

Throughout this book it has at least been implicit that consistency and asymptotic normality will ordinarily hold, under appropriate regularity conditions, just as for the case of ordinary likelihood. Sometimes we have been quite explicit about this expectation, such as with the meta theorem enunciated in Chapter 4. We have chosen not to attempt a substantiation of these principles because of the elusiveness of a satisfying general statement and the delicacy of the results as exercises in mathematics as distinct from the reality of practically relevant examples. Also, we have made it clear already that it is generally preferable to check directly, in any particular example, for consistency and asymptotic normality, rather than trying to check the conditions of a special purpose theorem.