Large-Sample Theory

In this chapter, we discuss large sample theory that can be applied under conditions that are quite likely to be met in large samples even when the Gauss–Markov conditions are broken. There are two reasons for using large sample theory. First, there may be some problems that corrupt our estimators in small samples but tends to diminish down as the sample gets bigger. Thus, if we cannot get a perfect small sample estimator, we will usually want to choose the one that will be best in large samples. Second, in some circumstances, the theory used to derive the properties of estimators in small samples just does not work, and working out the properties of the estimators can be impossible. This makes it very hard to choose between alternative estimators. In these circumstances we judge different estimators on their “large sample properties” because their “small (or finite) sample properties” are unknown.