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The geometry of case deletion and the assessment of influence in nonlinear regression
Author(s) -
Ross William H.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315198
Subject(s) - nonlinear system , estimator , mathematics , nonlinear regression , contrast (vision) , extension (predicate logic) , linear regression , regression , regression analysis , linear model , proper linear model , statistics , mathematical optimization , algorithm , computer science , artificial intelligence , polynomial regression , physics , quantum mechanics , programming language
Numerous influence measures are available for use in linear regression. By contrast, very little has been done for nonlinear models. A notable exception is Chapter 4 of Cook and Weisberg (1982). The extension of measures based on case deletion from the linear to the nonlinear model usually involve linear approximation. In this paper, the geometry of case deletion is studied with a view to assessing the adequacy of linear approximation in the construction of influence measures for nonlinear regression. Of particular interest is the adequacy of the one‐step estimator for the jack‐knifed pseudoestimates of the unknown parameter vector.