JSM 2004 - Toronto

Abstract #302140

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Activity Number: 86
Type: Contributed
Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #302140
Title: Simulation as an Alternative to the Delta Method
Author(s): Patrick R. Johnston*+
Companies: Abt Associates Inc.
Address: 55 Wheeler St., Cambridge, MA, 02138,
Keywords: delta method
Abstract:

This paper addresses the situation where the data comprise a collection of parameter estimates along with their standard errors. The goal of the analysis is to obtain a confidence interval for a function of these parameters. Problems of this nature are commonly solved via the delta method, whereby the function of interest is approximated by a linear function and a confidence interval is obtained for the latter. The appropriateness of the resulting confidence interval depends on the appropriateness of the linear approximation. We propose a simple alternative based on simulating the density of the function and obtaining a Bayesian probability interval which may then be interpreted in a frequentist fashion. The resulting interval estimate is attractive from frequentist, likelihood, and Bayesian perspectives. The method was applied to a problem involving the estimation of cocaine production from South America.

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Revised March 2004