  We consider semiparametric moment condition models invariant to
transformation groups. The parameter of interest is estimated by minimum
empirical divergence approach, introduced by Broniatowski and Keziou (2012). It
is shown that the minimum empirical divergence estimates, including the
empirical likelihood one, are equivariants. The minimum risk equivariant
estimate is then identied to be any one of the minimum empirical divergence
estimates minus its expectation conditionally to maximal invariant statistic of
the considered group of transformations. An asymptotic approximation to the
conditional expectation, is obtained, using the result of Jureckov{\'a} and
Picek (2009).
