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Confidence bounds for the extremum determined by a quadratic regression

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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

Suggested Citation

  • Jenny Lye & Joe Hirschberg, 2004. "Confidence bounds for the extremum determined by a quadratic regression," Econometric Society 2004 Australasian Meetings 217, Econometric Society.
    • Handle: RePEc:ecm:ausm04:217
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    More about this item

    Keywords

    Turning Point; Fieller interval; U-shaped;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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