Briefly, let
be an
matrix with element
, where the indicator function
takes the value one if observation
belongs to group
with
, and zero otherwise (we drop the columns for the groups with
to avoid singularity). Let
be the
matrix of the contributions to the score
. The Andrews test statistic is
times the
from regressing a constant (one) on each column of
and
. Under the null hypothesis that the model is correctly specified,
is asymptotically distributed
with
degrees of freedom.