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Distribution free testing for conditional distributions given covariates. (English) Zbl 1379.62036
Summary: Given a sample \((\xi_i,X_i)_{i=1}^n\) of i.i.d. pairs, consider \(F_x\) and \(Q_x\) as two different models for conditional distribution of \(\xi_i\) given \(X_i=x\). The paper shows how the empirical process for testing \(F_x\) can be transformed into a process with the same asymptotic behavior as the empirical process for testing \(Q_x\) thereby rendering the two testing problems equivalent.

MSC:
62G10 Nonparametric hypothesis testing
62F03 Parametric hypothesis testing
62F05 Asymptotic properties of parametric tests
62G20 Asymptotic properties of nonparametric inference
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