JSM 2004 - Toronto

Abstract #300354

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Activity Number: 360
Type: Invited
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: SSC
Abstract - #300354
Title: Shift Function Plots for Regression Fitting
Author(s): David Bellhouse*+ and Zilin Wang
Companies: University of Western Ontario and University of Western Ontario
Address: Dept. of Statistics and Actuarial Science, London, ON, N6A 5B7, Canada
Keywords: parametric and nonparametric regression ; bootstrapping
Abstract:

Although a nonparametric regression model allows us to obtain a graphical display of the functional relationship between the response and independent variables, the exact form of the regression function is not evident. Such a functional relationship is explicit in a parametric model. Our objective is to introduce a new graphical approach, called the shift function plot, with which a hypothesis is constructed to evaluate the goodness of fit of a parametric regression model. We parameterize the model under the null hypothesis. Then we use the nonparametric representation as the unrestricted regression model through which we examine how well the parametric model fits the data. Inferential issues relating to the shift functions are examined and a chi-square test statistic is developed with the aid of bootstrapping.

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