On the asymptotic distribution of the likelihood ratio statistic

Likelihood ratio tests are among the most frequently used in practical statistics. Important references on this subject include Wilks (1962), Rao (1965, pp. 347-352), and Agresti (1990, pp. 434-435). We give proofs of some well-known results on the limiting distribution of D = -2 log(lambda), where lambda is the likelihood ratio, under certain clearly-stated assumptions. We illustrate the theory by means of an example on contingency tables. Although results of this type are frequently used, the underlying theory is not always fully explained.