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The Null Distribution of the Empirical AUC for Classi ers with Estimated Parameters: a Special Case

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Abstract

We study the distribution of the area under an empirical receiver operating characteristic (ROC) curve constructed from a first stage regression model with parameters estimated on the same data set. We provide a general, but somewhat intrinsic, characterization of the limit distribution of this area, denoted AUC, when the regressors are Bernoulli random variables jointly independent of the outcome. Using the general theory, we further analyze the limit distribution in the two regressor case. It is non-normal and right-skewed. Though the theory applies, explicit expressions for the limit distribution are cumbersome to write down for a larger number of regressors. We provide a trivariate example as further illustration.

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  • Robert P. Lieli & Yu-Chin Hsu, 2016. "The Null Distribution of the Empirical AUC for Classi ers with Estimated Parameters: a Special Case," IEAS Working Paper : academic research 16-A007, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:16-a007
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    Keywords

    binary classification; ROC curve; area under the ROC curve; overfitting; hypothesis testing; model selection;
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