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WHEN LEAST‐SQUARES SQUARES LEAST 1
Author(s) -
ALCHALABI M.
Publication year - 1992
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1992.tb00380.x
Subject(s) - least squares function approximation , goodness of fit , explained sum of squares , statistics , total least squares , residual sum of squares , mathematics , lack of fit sum of squares , square root , non linear least squares , least trimmed squares , mean squared error , simple (philosophy) , computer science , regression analysis , geometry , philosophy , epistemology , estimator
A bstract There is a general lack of awareness among ‘lay’ professionals (geophysicists included) regarding the limitations in the use of least‐squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least‐squares and other goodness‐of‐fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least‐squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least‐squares is one of the worst criteria to use. In such cases, data treatment, ‘robust statistics’ or similar processes provide an alternative approach.