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Non‐parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise

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  • AXEL MUNK
  • NATALIE NEUMEYER
  • ACHIM SCHOLZ

Abstract

. The purpose of this paper was to propose a procedure for testing the equality of several regression curves fi 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 fi. 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.

Suggested Citation

  • Axel Munk & Natalie Neumeyer & Achim Scholz, 2007. "Non‐parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 511-534, September.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:3:p:511-534
    DOI: 10.1111/j.1467-9469.2006.00535.x
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Debajit Chatterjee & Uttam Bandyopadhyay, 2019. "Testing in nonparametric ANCOVA model based on ridit reliability functional," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 327-364, April.
    3. Lyubchich, Vyacheslav & Gel, Yulia R., 2016. "A local factor nonparametric test for trend synchronism in multiple time series," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 91-104.

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