ISBIS4 Abstract

Contact Author's Name: Ali S. Hadi
Title of Abstract: Local Sensitivity Analysis in Estimation Problems
Author(s): Ali S. Hadi
Affiliation: American University in Cairo

This paper deals with the problem of local sensitivity analysis, i.e., how much a change in the data modifies the results of a statistical analysis. A general methodology which is applicable to any statistical problem that can be expressed as an optimization problem or that involves solving a system of equations is applied to some statistical problems. As some particular examples, we apply it to the maximum likelihood method and the standard and constrained methods of moments. Unlike the standard method of moments, constrained method of moments ensures that the obtained estimates are always consistent with the data. Closed analytical formulas for the calculation of these local sensitivities are derived. The obtained sensitivities include: (a) the objective function sensitivities to data points and (b) the sensitivities of the estimated parameters to data points. The derived formulas for the sensitivities are based on recent results in the area of mathematical programming. Several examples of parameter estimation problems are used to illustrate the methodology.