Basic Sequences and Unbiased Estimation in Quasi Power Series Distributions

Abstract

By using results from function space theory we give a characterization of when lacunary quasi power series sequences are basic in C[0, 1]. The paper discusses the links with unbiased estimable functions and the subspaces generated by the density of the lacunary quasi power series distributions. The paper also provides the rates of convergence of all the moments of the classic odds ratio estimator. This extends some known results in Bleimann, Butzer and Hahn's approximation operator.