Abstract #301602

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JSM 2003 Abstract #301602
Activity Number: 423
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #301602
Title: Estimating the Location of the Maximum or Minimum Response When the Function is Not Necessarily Quadratic
Author(s): Philip M. Dixon*+ and Wuyan Zhang
Companies: Iowa State University and Iowa State University
Address: Dept. of Statistics, Ames, IA, 50011-0001,
Keywords: dose-response curve ; nonparametric regression
Abstract:

When a response function, Y=f(x), is quadratic, the location of the maximum or minimum is easy to estimate. Confidence intervals for the location can be constructed using Fieller's theorem, the delta method, or bootstrapping. Here, we consider estimating the location of the maximum when f(x) may not be quadratic. One example is the hypocholesterolemic effect of sheanut oil. The dose-response curve is nonmonotonic. We develop three methods for estimating the location of the maximum or minimum. Two are based on a power transformation of x; the third is based on nonparametric regression. Confidence intervals can be constructed using profile likelihood or bootstrapping. These methods are illustrated using the sheanut data.

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