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.
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Acknowledgements
For the results, shown in Figs. 2, 3, 4 and 5 and many more experiments, not included here, the author is grateful to his student at the time, Richard White. Author is also grateful to the referees for patience with many imperfections of the initial draft and for the number of useful advice. Careful reading by Sara Algeri greatly helped to improve the text at the final stages.
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Khmaladze, E.V. Distribution-free testing in linear and parametric regression. Ann Inst Stat Math 73, 1063–1087 (2021). https://doi.org/10.1007/s10463-021-00786-3
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DOI: https://doi.org/10.1007/s10463-021-00786-3