Exact Optimal Inference in Regression Models under Heteroskedasticity and Non-Normality of Unknown Form Articles uri icon


  • DUFOUR, J. M.

publication date

  • November 2010

start page

  • 2532

end page

  • 2553


  • 11


  • 54

International Standard Serial Number (ISSN)

  • 0167-9473

Electronic International Standard Serial Number (EISSN)

  • 1872-7352


  • Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesis considered, an adaptive approach based on a split-sample technique is proposed in order to choose an alternative that brings power close to the power envelope. The performance of the proposed quasi-point-optimal sign tests with respect to size and power is assessed in a Monte Carlo study. The power of quasi-point-optimal sign tests is typically close to the power envelope, when approximately 10% of the sample is used to estimate the alternative and the remaining sample to compute the test statistic. Further, the proposed procedures perform much better than common least-squares-based tests which are supposed to be robust against heteroskedasticity.