Efficient Likelihood Ratio Confidence Intervals using Constrained Optimization

17 Pages Posted: 26 Sep 2019 Last revised: 10 Dec 2020

See all articles by Gregor Reich

Gregor Reich

Tsumcor Research AG

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP); National Bureau of Economic Research (NBER)

Date Written: December 9, 2020

Abstract

Using constrained optimization, we develop a simple, efficient approach (applicable in both unconstrained and constrained maximum-likelihood estimation problems) to computing profile-likelihood confidence intervals. In contrast to Wald-type or score-based inference, the likelihood ratio confidence intervals use all the information encoded in the likelihood function concerning the parameters, which leads to improved statistical properties. In addition, the method does no suffer from the computational burdens inherent in the bootstrap. In an application to Rust's (1987) bus-engine replacement problem, our approach does better than either the Wald or the bootstrap methods, delivering very accurate estimates of the confidence intervals quickly and efficiently. An extensive Monte Carlo study reveals that in small samples, only likelihood ratio confidence intervals yield reasonable coverage properties, while at the same time discriminating implausible values.

Suggested Citation

Reich, Gregor and Judd, Kenneth L., Efficient Likelihood Ratio Confidence Intervals using Constrained Optimization (December 9, 2020). Available at SSRN: https://ssrn.com/abstract=3455484 or http://dx.doi.org/10.2139/ssrn.3455484

Gregor Reich (Contact Author)

Tsumcor Research AG ( email )

Switzerland

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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