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 a chisquared variable with J degrees of freedom. Conclude that in the generalized regression model, the limiting distribution of the Wald statistic

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.

Transcribed Image Text:

W = (Rß – q)'{R(Est. Var[ß])R'}¯'(Rß – q) %3D