Inferences for the Extremum of Quadratic Regression Models

23 Pages Posted: 25 Jul 2006

See all articles by Joe Hirschberg

Joe Hirschberg

University of Melbourne - Department of Economics

Jenny N. Lye

University of Melbourne - Department of Economics

Date Written: October 2005

Abstract

Quadratic functions are often used in regression to infer the existence of an extremum in a relationship although tests of the location of the extremum are rarely performed. We investigate the construction of the following confidence intervals: Delta, Fieller, estimated first derivative, bootstrapping, Bayesian and likelihood ratio. We propose interpretations for the unbounded intervals that may be generated by some of these methods. The coverage of the confidence intervals is assessed by Monte Carlo; the Delta and studentized bootstrap can perform quite poorly. Of all the methods, the first derivative method is easiest to implement.

Keywords: Inverted U-Shaped, turning point, Fieller method, Delta method, 1st derivative function, Bayesian, Likelihood ratio, Bootstrap

JEL Classification: C21, C40, C52

Suggested Citation

Hirschberg, Joseph G. and Lye, Jenny N., Inferences for the Extremum of Quadratic Regression Models (October 2005). Available at SSRN: https://ssrn.com/abstract=918626 or http://dx.doi.org/10.2139/ssrn.918626

Joseph G. Hirschberg (Contact Author)

University of Melbourne - Department of Economics ( email )

Victoria 3010, 3010
Australia

Jenny N. Lye

University of Melbourne - Department of Economics ( email )

Melbourne, 3010
Australia

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