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Consistent selection of explanatory variables

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  • Herman J. Bierens

Abstract

We consider a linear regression model where some explanatory variables are unknown members of sets of alternative explanatory variables. It will be shown that under weak conditions the minimum residual variance criterion for selecting these explanatory variables has the property that the probability of selecting wrong explanatory variables vanishes if the number of observations increases to infmity. Moreover, the O.L.S. estimator of the resulting “specified” model turns out to be consistent, while in the case that all the parameters are nonzero it can be shown that this O.L.S. estimator has the same limiting distribution as the O.L.S. estimator of the true model.

Suggested Citation

  • Herman J. Bierens, 1980. "Consistent selection of explanatory variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(3), pages 141-150, September.
    • Handle: RePEc:bla:stanee:v:34:y:1980:i:3:p:141-150
    DOI: 10.1111/j.1467-9574.1980.tb00696.x
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