Inferences for the Extremum of Quadratic Regression Models

Joseph Hirschberg and Jeanette Lye

No 906, Department of Economics - Working Papers Series from The University of Melbourne

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. (search for similar items in EconPapers)
JEL-codes: C21 C40 C52 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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