Robust Semiparametric Estimation in the Presence of Heterogeneity of Unknown Form

We show that semiparametric adaptive maximum likelihood estimators have desirable robustness properties when the innivations in a location parameter model are uncorrelated but not necessarily independent. We show that such estimators have asymptotic covariance matrices equal to the inverse of the Fisher information of the unconditional distribution of the data in the presence of general forms of heterogeneity, including conditional dependence in even moments.