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Robust Wald tests in SUR systems with adding-up restrictions. (English) Zbl 1016.62074
From the introduction: We consider SUR systems with adding-up restrictions where the same explanatory variables are present in all equations and where heteroskedasticity and/or autocorrelation of unknown forms may be present. For this case, the coefficients are usually estimated by least squares, equation by equation. For testing the typical hypotheses of interest, we show that the robust Wald statistic, i.e., the statistic based on the heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator, is invariant to the equation deleted. Our proof of invariance does not rely on parametric assumptions or on knowledge of the covariance matrix. The weighted sum of the dependent variables in this paper adds up to one of the explanatory variables, not necessarily a constant. Our proof exploits the properties of generalized inverses and depends only on the existence of first and second moments. It should be noted that even though our robust Wald test is invariant to the equation deleted, it is not invariant to nonlinear transformations of the null hypothesis.

##### MSC:
 62H15 Hypothesis testing in multivariate analysis 62F35 Robustness and adaptive procedures (parametric inference) 62P20 Applications of statistics to economics 62J05 Linear regression; mixed models
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