Publication: Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms
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2008-11
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Abstract
In this paper, we derive simple point-optimal sign-based tests in the context of linear and
nonlinear regression models with fixed regressors. These tests are exact, distribution-free, robust
against heteroskedasticity of unknown form, and they may be inverted to obtain confidence
regions for the vector of unknown parameters. Since the point-optimal sign tests depend on the
alternative hypothesis, we propose an adaptive approach based on split-sample techniques in
order to choose an alternative such that the power of point-optimal sign tests is close to the
power envelope. The simulation results show that when using approximately 10% of sample to
estimate the alternative and the rest to calculate the test statistic, the power of point-optimal sign
test is typically close to the power envelope. We present a Monte Carlo study to assess the
performance of the proposed “quasi”-point-optimal sign test by comparing its size and power to
those of some common tests which are supposed to be robust against heteroskedasticity. The
results show that our procedures are superior.
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Keywords
Sign test, Point-optimal test, Nonlinear model, Heteroskedasticity, Exact inference, Distribution-free, Power envelope, Split-sample, Adaptive method, Projection