Inferences for the Extremum of Quadratic Regression Models
AbstractQuadratic 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.
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Bibliographic InfoPaper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 906.
Length: 24 pages
Date of creation: 2004
Date of revision:
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Inverted U-Shaped; turning point; Fieller method; Delta method; 1st derivative function; Bayesian; Likelihood ratio; Bootstrap.;
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