Heteroskedasticity-Robust Tests in Regressions Directions

Davidson,; MacKinnon,

doi:10.2307/20076563

Cited by 85 publications

(71 citation statements)

References 16 publications

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“…Given the independence of the observations,Ω n,m should be a diagonal matrix of squared residuals. For heteroscedasticity-robust testing, the literature frequently recommends using the residuals of the model under the null hypothesis; see, e.g., Davidson and MacKinnon (1985). Hence, I use the residualsû i,m := y i − x i,mβ m and definê Ω n,m := diag(û 2 1,m , .…”

Section: The Mj Test For Non-nested Regression Modelsmentioning

confidence: 99%

A simple test for regression specification with non-nested alternatives

Hagemann

2012

Journal of Econometrics

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Section: The Mj Test For Non-nested Regression Modelsmentioning

confidence: 99%

A simple test for regression specification with non-nested alternatives

Hagemann

2012

Journal of Econometrics

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“…The above algorithm is simply a discretized approximation to the operator K. As such, each estimateK is subject to some approximation error that shrinks as the size of the partition (m) increases. Wooldridge (1990), extending the work of Davidson and MacKinnon (1985) in the context of robustifying regression specification tests, proposed a projection technique that achieves the same goal as the martingale transform -it accounts for the effect of estimation and leaves statistics asymptotically distribution-free. Khmaldaze's martingale transform bears a good deal of similarity to Wooldridge's proposal.…”

Section: Computation Of the Compensatormentioning

confidence: 99%

A Comparison of Alternative Approaches to Supremum-Norm Goodness of Fit Tests with Estimated Parameters

Parker

2012

SSRN Journal

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Goodness of fit tests based on empirical processes have nonstandard limiting distributions when the null hypothesis is composite -that is, when parameters of the null model are estimated. Several solutions to this problem have been suggested, including the calculation of adjusted critical values for these nonstandard distributions and the transformation of the empirical process such that statistics based on the transformed process are asymptotically distribution-free. The approximation methods proposed by Durbin (1985) can be applied to compute appropriate critical values for tests based on supremum-norm statistics. The resulting tests have quite accurate size, a fact which has gone unrecognized in the econometrics literature. Some justification for this accuracy lies in the similar features that Durbin's approximation methods share with the theory of extrema for Gaussian random fields and for Gauss-Markov processes. These adjustment techniques are also related to the transformation methodology proposed by Khmaladze (1981) through the score function of the parametric model. Simulation experiments suggest that these two testing strategies are roughly comparable to one another and more powerful than a simple bootstrap procedure.

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“…Explicitly, Σ Ω̃ is given by 1 Available: http://www.fil.ion.ucl.ac.uk/spm/ (6) where and εt is the tth component of ε̃ as given in (8). Various simulation studies have shown that the use of ε̃ leads to a better control of Type I error rates [34], [38].…”

Section: A Heteroscedastic Linear Model and A Wald-type Test Statisticmentioning

confidence: 99%

A Statistical Analysis of Brain Morphology Using Wild Bootstrapping

Zhu

Ibrahim

Tang

et al. 2007

IEEE Trans. Med. Imaging

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Methods for the analysis of brain morphology, including voxel-based morphology and surfacebased morphometries, have been used to detect associations between brain structure and covariates of interest, such as diagnosis, severity of disease, age, IQ, and genotype. The statistical analysis of morphometric measures usually involves two statistical procedures: 1) invoking a statistical model at each voxel (or point) on the surface of the brain or brain subregion, followed by mapping test statistics (e.g., t test) or their associated p values at each of those voxels; 2) correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation. We propose the use of new statistical methods for each of these procedures. We first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion (e.g., cortical or subcortical surfaces) and the covariates of interest. Moreover, we develop a robust test procedure that is based on a resampling method, called wild bootstrapping. This procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest. The value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data, including data from both anatomical and functional magnetic resonance imaging (fMRI). Simulation studies demonstrate that this robust test procedure can accurately control the family-wise error rate. We demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects.

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Heteroskedasticity-Robust Tests in Regressions Directions

Cited by 85 publications

References 16 publications

A simple test for regression specification with non-nested alternatives

A simple test for regression specification with non-nested alternatives

A Comparison of Alternative Approaches to Supremum-Norm Goodness of Fit Tests with Estimated Parameters

A Statistical Analysis of Brain Morphology Using Wild Bootstrapping

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