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Keywords:
robust regression; autocorrelated errors; heteroscedastic regression; instrumental variables; least weighted squares
robust regression; autocorrelated errors; heteroscedastic regression; instrumental variables; least weighted squares
Summary:
Highly robust statistical and econometric methods have been developed not only as a diagnostic tool for standard methods, but they can be also used as self-standing methods for valid inference. Therefore the robust methods need to be equipped by their own diagnostic tools. This paper describes diagnostics for robust estimation of parameters in two econometric models derived from the linear regression. Both methods are special cases of the generalized method of moments estimator based on implicit weighting of individual observations. This has the effect of down-weighting less reliable observations and ensures a high robustness and low sub-sample sensitivity of the methods. Firstly, for a robust regression method efficient under heteroscedasticity we derive the Durbin–Watson test of independence of random regression errors, which is based on the approximation to the exact null distribution of the test statistic. Secondly we study the asymptotic behavior of the Durbin–Watson test statistic for the weighted instrumental variables estimator, which is a robust analogy of the classical instrumental variables estimator.
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