Unbiased estimation of von Mises functionals

We construct minimum variance unbiased estimators of von Mises functionals in estimation problems where no complete sufficient [sigma]-algebra exists. The construction method is instead based on the higher order tangent structure of the underlying class of distributions. We discuss especially some curved and some noncurved nonparametric examples in the iid case and estimation in nonparametric Markov chain models.k-tangent vector unbiased estimation symmetry model Markov chain