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Non‐parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise
Author(s) -
MUNK AXEL,
NEUMEYER NATALIE,
SCHOLZ ACHIM
Publication year - 2007
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.1467-9469.2006.00535.x
Subject(s) - mathematics , heteroscedasticity , statistics , test statistic , estimator , nuisance parameter , asymptotic distribution , context (archaeology) , parametric statistics , statistic , regression analysis , ordinary least squares , econometrics , statistical hypothesis testing , paleontology , biology
. The purpose of this paper was to propose a procedure for testing the equality of several regression curves f i in non‐parametric regression models when the noise is inhomogeneous and heteroscedastic, i.e. when the variances depend on the regressor and may vary between groups. The presented approach is very natural because it transfers the maximum likelihood statistic from a heteroscedastic one‐way analysis of variance to the context of non‐parametric regression. The maximum likelihood estimators will be replaced by kernel estimators of the regression functions f i . It is shown that the asymptotic distribution of the obtained test‐statistic is nuisance parameter free. Asymptotic efficiency is compared with a test of Dette & Neumeyer [Annals of Statistics (2001) Vol. 29, 1361–1400] and it is shown that the new test is asymptotically uniformly more powerful. For practical purposes, a bootstrap variant is suggested. In a simulation study, level and power of this test will be briefly investigated and compared with other procedures. In summary, our theoretical findings are supported by this study. Finally, a crop yield experiment is reanalysed.