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Testing Independence of Covariates and Errors in Non‐parametric Regression

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  • Subhra Sankar Dhar
  • Wicher Bergsma
  • Angelos Dassios

Abstract

Consider a non‐parametric regression model Y=m(X)+ϵ, where m is an unknown regression function, Y is a real‐valued response variable, X is a real covariate, and ϵ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ϵ. Further, we investigate the local power of the proposed tests using Le Cam's contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows that the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets.

Suggested Citation

  • Subhra Sankar Dhar & Wicher Bergsma & Angelos Dassios, 2018. "Testing Independence of Covariates and Errors in Non‐parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 421-443, September.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:3:p:421-443
    DOI: 10.1111/sjos.12301
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