Unbiased estimation of von Mises functionals (Q1093275)

In this work the author constructs minimum variance unbiased estimators (MVUE) of von Mises functionals in estimation problems where no complete sufficient \(\sigma\)-algebra exists. The construction method is based on the higher order tangent structure of the underlying class of distributions. The main result of the paper is a modification of Barankin's characterization of MVUE which is especially suitable for nonparametric models; see \textit{E. W. Barankin}, Ann. math. Stat. 20, 477-501 (1949; Zbl 0034.230). The work discusses especially some curved and some noncurved nonparametric models in the i.i.d. case and estimation in nonparametric Markov chain models.