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On Sensitivity of Inverse Response Plot Estimation and the Benefits of a Robust Estimation Approach
Author(s) -
PRENDERGAST LUKE A.,
SHEATHER SIMON J.
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00807.x
Subject(s) - mathematics , transformation (genetics) , linearization , inverse , ordinary least squares , sensitivity (control systems) , estimation theory , function (biology) , least squares function approximation , nonlinear regression , plot (graphics) , estimation , statistics , nonlinear system , regression analysis , biochemistry , chemistry , physics , geometry , quantum mechanics , electronic engineering , evolutionary biology , biology , engineering , gene , management , economics , estimator
. Inverse response plots are a useful tool in determining a response transformation function for response linearization in regression. Under some mild conditions it is possible to seek such transformations by plotting ordinary least squares fits versus the responses. A common approach is then to use nonlinear least squares to estimate a transformation by modelling the fits on the transformed response where the transformation function depends on an unknown parameter to be estimated. We provide insight into this approach by considering sensitivity of the estimation via the influence function. For example, estimation is insensitive to the method chosen to estimate the fits in the initial step. Additionally, the inverse response plot does not provide direct information on how well the transformation parameter is being estimated and poor inverse response plots may still result in good estimates. We also introduce a simple robustified process that can vastly improve estimation.