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THE GROUPING PROBLEM IN DISTRIBUTION‐FREE PLANAR REGRESSION
Author(s) -
Brown B.M.,
Pella M.J.
Publication year - 1991
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1991.tb00441.x
Subject(s) - mathematics , independent and identically distributed random variables , simple (philosophy) , distribution (mathematics) , statistics , regression analysis , regression , reduction (mathematics) , nuisance parameter , linear regression , inference , planar , mathematical optimization , computer science , random variable , mathematical analysis , artificial intelligence , geometry , philosophy , computer graphics (images) , epistemology , estimator
Summary In the planar regression model having two slope parameters and identically distributed errors, exact distribution‐free inference about one parameter may be carried out by grouping the observations, eliminating the nuisance parameter and reducing the model to simple linear regression, allowing exact distribution‐free methods for slope to be employed. This model reduction involves a loss of efficiency: the choice of an optimal grouping to minimize efficiency loss is discussed.