Extension of the Parametric Delta Method with an Application to an Inference Method for a Degradation Model

The delta method is a powerful method to approximate the probability distribution of a function $$\phi$$ ϕ of an asymptotically normal statistical estimator $$T_n$$ Tn where nis the sample size. Generally the asymptotic normality of the estimator results from central limit theorems that requires to center $$T_n$$ Tn and the function $$\phi$$ ϕ does not depend on n. In this paper, we provide an extension of the classical delta method to the case where both the centering parameter and the function $$\phi$$ ϕ depend on the sample size. This method can be used in various statistical applications (repeated measurement, panel data, degradation data, etc.). Starting by pointing out the main classical parametric delta methods, we provide its extension. The extended delta method is illustrated by an application to degradation data where the unknown parameters are estimated using the method of moments.