Abstract
The following proposition is sometimes used in distribution theory: for each fixed $z$ suppose that $T(X, z)$ has the distribution $Q$ and is independent of $Y$; then $T(X, Z(Y))$ has the distribution $Q$ and is independent of $Y$. An example is presented to show this result is false in general. Additional conditions under which the proposition becomes valid are presented.
Citation
Michael D. Perlman. Michael J. Wichura. "A Note on Substitution in Conditional Distribution." Ann. Statist. 3 (5) 1175 - 1179, September, 1975. https://doi.org/10.1214/aos/1176343248
Information
