The Lagrange multiplier test of the hypothesis R q = 0 is equivalent to a Wald test of
Chapter 6, Problem 7(choose chapter or problem)
The Lagrange multiplier test of the hypothesis R q = 0 is equivalent to a Wald test of the hypothesis that = 0, where is defined in (6-14). Prove that 2 = Est. Var[] 1 = (n K) e e e e 1 . Note that the fraction in brackets is the ratio of two estimators of 2. By virtue of (6-19) and the preceding discussion, we know that this ratio is greater than 1. Finally, prove that the Lagrange multiplier statistic is equivalent to JF, where J is the number of restrictions being tested and F is the conventional F statistic given in (6-6).
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