Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Jean-Marie Dufour () and Abderrahim Taamouti

Computational Statistics & Data Analysis, 2010, vol. 54, issue 11, 2532-2553

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.

Keywords: Sign; test; Point-optimal; test; Nonlinear; model; Heteroskedasticity; Exact; inference; Distribution-free; Power; envelope; Split-sample; Adaptive; method; Projection (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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