Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form |
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Authors: | Jean-Marie Dufour Abderrahim Taamouti |
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Affiliation: | a William Dow Professor of Economics, McGill University, Canada b Centre interuniversitaire de recherche en analyse des organisations (CIRANO), Canada c Centre interuniversitaire de recherche en économie quantitative (CIREQ), Canada d Economics Department, Universidad Carlos III de Madrid, Spain |
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Abstract: | 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. |
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Keywords: | Sign test Point-optimal test Nonlinear model Heteroskedasticity Exact inference Distribution-free Power envelope Split-sample Adaptive method Projection |
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