Now suppose that the disturbances are not normally distributed, although is still known. Show that the limiting distribution of previous statistic is (1/J) times

Now suppose that the disturbances are not normally distributed, although Ω is still known. Show that the limiting distribution of previous statistic is (1/J) times a chisquared variable with J degrees of freedom. Conclude that in the generalized regression model, the limiting distribution of the Wald statistic W = (Rβ − q)'{R(Est.Var[β])R'}−1 (Rβ − q) is chi-squared with J degrees of freedom, regardless of the distribution of the disturbances, as long as the data are otherwise well behaved. Note that in a finite sample, the true distribution may be approximated with an F[J, n − K] distribution. It is a bit ambiguous, however, to interpret this fact as implying that the statistic is asymptotically distributed as F with J and n− K degrees of freedom, because the limiting distribution used to obtain our result is the chi-squared, not the F. In this instance, the F[J, n − K] is a random variable that tends asymptotically to the chi-squared variate.