an:06821217
Zbl 1379.62036
Khmaladze, Estate
Distribution free testing for conditional distributions given covariates
EN
Stat. Probab. Lett. 129, 348-354 (2017).
00372838
2017
j
62G10 62F03 62F05 62G20
unitary operators; empirical process; Kiefer process; parametric models; orthogonal projections
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.