Multivariate Application Domains for the Delta Method

Abstract

Given statistics with components Yi = gi(μ +X), i = 1, ...,m, and domains D such that, when μ ∈ D, distributions derived applying to Delta method may be used. The case in which X is normal is singled out. Then the approximate distributions are normal and may be applied in situations with high non-centrality parameter Δ = μtΣ−1μ where Σ is the variance-covariance matrix of X.