Maria Croppenstedt <mariacroppenstedt@hotmail.com> asked about the
distribution of the boundary LR test produced by -frontier-.
She noted that
> The help explanation implies that the test is based on the assumption that
> the inefficiency term is "a 50:50 mixture of a chisquare with no degrees of
> freedom (i.e. a point mass at zero) and a chisquare with 1 degree of
> freedom."
But then she went on to say that this result was not intuitive, because
the inefficiency disturbances are assumed to have a half-normal
distribution.
It is not the form of the distribution of the inefficiency disturbances
but rather the distribution of the estimator that gives rise to the
mixed-chi-squared distribution. The estimator of the standard deviation
sigma is bounded at zero, it cannot be any smaller than zero. The fact
that the estimator is bounded at zero makes the distribution of the LR
test of sigma=0 have some point mass at zero.
--David
ddrukker@stata.com
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