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For example :in Econometric models like Tobit regression and Censored regression models
Do you mean the Durbin–Wu–Hausman test (augmented regression test) for endogeneity? I don't think there is a credible alternate test (I could be wrong) but this is what I use..
Edit: I found this on the net: http://www.emeraldinsight.com/doi/abs/10.1108/S%282012%(The Hausman Test, and Some Alternatives, with Heteroskedastic Data)
Basically the authors of the paper have devised some new tests that you can use (but they are not "standard" or well used in the market)