Application domains for the Delta method

Abstract

The Delta method uses truncated Lagrange expansions of statistics to obtain approximations to their distributions. In this paper, we consider statistics Y=g(μ+X), where X is any random vector. We obtain domains 𝒟 such that, when μ∈𝒟, we may apply the distribution derived from the Delta method. Namely, we will consider an application on the normal case to illustrate our approach.

Keywords:

• Delta method
• asymptotic linear functions
• linear and quadratic forms
• polynomials
• normal distributions

Acknowledgements

The authors would like to thank the anonymous referees for useful comments and suggestions.