Confidence bounds for the extremum determined by a quadratic regression

Jeanette Ngaire Lye () and Joseph Gerald Hirschberg ()

No 217, Econometric Society 2004 Australasian Meetings from Econometric Society

Abstract: A quadratic function is frequently used in regression to infer the existence of an extremum in a relationship. Examples abound in fields such as economics, epidemiology and environmental science. However, most applications provide no formal test of the extremum. Here we compare the Delta method and the Fieller method in typical applications and perform a Monte Carlo study of the coverage of these confidence bounds. We find that unless the parameter on the squared term is estimated with great precision, the Fieller confidence interval may posses dramatically better coverage than the Delta method

Keywords: Turning Point; Fieller interval; U-shaped (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ifn
Date: Written 2004-08-11
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