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Pearson‐type goodness‐of‐fit tests for regression
Author(s) -
Akritas M. G.,
Torbeyns A. F.
Publication year - 1997
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 - 10.2307/3315784
Subject(s) - goodness of fit , mathematics , statistics , test statistic , statistic , normality , quadratic equation , linear regression , regression analysis , pearson's chi squared test , statistical hypothesis testing , geometry
A procedure for testing the goodness of fit of linear regression models is introduced. For a given partition of the real line into cells, the proposed test is a quadratic form based on the vector of observed minus expected frequencies of the residuals obtained by maximum‐likelihood estimation of the regression parameters. The quadratic form is of the same computational difficulty as the traditional Pearson‐type tests with uncensored data. A statistic based on only one cell is particularly easy to apply and is used for testing the normality assumption in a real data set from astronomy. A simulation study examines the finite‐sample properties of the proposed tests.