The Functional Delta Method for Deriving Asymptotic Distributions

The functional delta method for deriving asymptotic distributions is presented. Assuming our interest lies in where is an unknown, infinite‐dimensional parameter and is a known functional. Like the delta method the functional delta method allows to immediately obtain an approximation of the distribution of the plug‐in estimator through the asymptotic distribution of subject to (a) the asymptotic distribution of being known and (b) the existence of an appropriate functional derivative of at . This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data