Asymptotic Expansion of D-Risks for Hypothesis Testing in Bernoulli Scheme

Abstract

© 2018, Pleiades Publishing, Ltd. Currently there is not a single asymptotic expansion of d-risk of any statistical procedure. In this paper we present the asymptotic expansion of d-risk function of the optimal test for Bernoulli scheme. The expansion derivation is based on the Edgeworth series of the sufficient statistic for Bernoulli scheme and therefore it is applicable to any one-parametric exponential model.