Accession Number : ADA139239

Title :   Bias in Nonlinear Regression.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Cook,R D ; Tsai,C L ; Wei,B C

PDF Url : ADA139239

Report Date : Feb 1984

Pagination or Media Count : 31

Abstract : This document investigates the biases of the residuals and the maximum likelihood parameters estimates from standard, normal-theory nonlinear regression models. Emphasis is placed on determining the influence of individual cases on the biases and on understanding how the residual biases can affect the usefulness of standard diagnostic methods. It is shown that the various bias expressions in the literature are equivalent, that the biases in nonlinear regression can be studied usefully in the context of linear regression, and that diagnostic plots using residuals can be misleading because of substantial residual biases. For a class of partially nonlinear models, it is shown that the maximum intrinsic curvature is closely related to the residual expectations. Finally, the model associated with power transformations of single explanatory variables in linear regression is investigated in further detail and several numerical illustrations are presented. (Author)

Descriptors :   *Nonlinear analysis, *Regression analysis, *Bias, Mathematical models, Residuals, Maximum likelihood estimation, Parameters, Diagnosis(General), Curvature, Linear regression analysis, Approximation(Mathematics), Data acquisition

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE