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Distribution-free testing in linear and parametric regression

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  • Estate V. Khmaladze

    (Victoria University of Wellington)

Abstract

Recently, a distribution-free approach for testing parametric hypotheses based on unitary transformations has been suggested in Khmaladze (Ann Stat 41:2979–2993, 2013, Bernoulli 22:563–588, 2016) and further studied in Nguyen (Metrika 80:153–170, 2017) and Roberts (Stat Probab Lett 150:47–53, 2019). In this paper, we show that the transformation takes very simple form in distribution-free testing of linear regression. Then, we extend it to the general parametric regression with vector-valued covariates.

Suggested Citation

  • Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:6:d:10.1007_s10463-021-00786-3
    DOI: 10.1007/s10463-021-00786-3
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    References listed on IDEAS

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