ABSTRACT
A common problem in large sample theory is the following. Given a sequence of random vectors, {X n }, and given its limit law, say https://www.w3.org/1998/Math/MathML"> X n → L X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq280.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , find the limiting distribution of f(X n ) for a given function, f (x). The Slutsky Theorems provide a powerful technique for attacking this problem. For example, it gives a simple method for showing that the t-statistic for a sample from a distribution with finite variance is asymptotically normal, as we shall see.
