A History of the Delta Method and Some New Results

Use of the delta method in statistics and econometrics is ubiquitous. Its mention can be found in almost all advanced statistics and econometrics textbooks but mostly without any reference. It appears that nobody knows for certain when the first paper on the topic was published or how the idea was first conceived. A seemingly unrelated method to find the asymptotic variance of a statistic involving one or more nuisance parameters was given by Pierce (Ann. Stat10, 475–478 1982). In the first part of the paper a comprehensive review of the delta method is presented with the objective of unearthing its history. In the second part a comparative analytic study of the delta method with the Pierce method is presented.