WIAS Preprint No. 314, (1997)

Testing a linear hypothesis using Haar transform


  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62H25 62G10


  • regression model, Haar basis, hypothesis of linearity, nonparametric alternative




The paper is concerned with the problem of testing a linear hypothesis about regression function. New testing procedure based on the Haar transform is proposed which is adaptive to unknown smoothness properties of the underlying function. The results show that under mild conditions on the design and smoothness of the regression function, this procedure provides with the near optimal rate of testing.

Appeared in

  • Math. Methods Statist., 10, no. 4 (2001), pp. 465 - 497, with new title Data driven testing the fit of linear models

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