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The asymptotic distribution of the sum of weighted squared residual in binary choice models. A x2 test

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  • Windmeijer, F

Abstract

It is claimed by some authors that the distribution of the sum of weighted squared residuals, used as a goodness of fit measure in binary choice models, behaves for large n as a x2n_k_i distribution. This claim seems to be based on a false analogy with the well-known Pearson x2 statistic for frequency tables with a fixed number of cells and cell sizes tending to infinity. We derive the asymptotic (normal) distribution and show that the approximation by the x2 distribution in general will not be valid. A new x2 test is proposed based on the asymptotic normality of the measure.

Suggested Citation

  • Windmeijer, F, 1989. "The asymptotic distribution of the sum of weighted squared residual in binary choice models. A x2 test," University of Amsterdam, Actuarial Science and Econometrics Archive 293145, University of Amsterdam, Faculty of Economics and Business.
    • Handle: RePEc:ags:amstas:293145
    DOI: 10.22004/ag.econ.293145
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    Research Methods/ Statistical Methods;

    Statistics

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