An implicit function based procedure for analyzing maximum likelihood estimates from nonidentically distributed data

Abstract

A methodology is presented for gaining insight into properties — such as outlier influence, bias, and width of confidence intervals — of maximum likelihood estimates from nonidentically distributed Gaussian data. The methodology is based on an application of the implicit function theorem to derive an approximation to the maximum likelihood estimator. This approximation, unlike the maximum likelihood estimator, is expressed in closed form and thus it can be used in lieu of costly Monte Carlo simulation to study the properties of the maximum likelihood estimator.

Keywords:

• maximum likelihood
• implicit function theorem
• non-i.i.d.
• influence function
• outliers
• sensitivity analysis
• bias
• confidence interval
• Taylor series