A Note on Substitution in Conditional Distribution
Perlman, Michael D. ; Wichura, Michael J.
Ann. Statist., Tome 3 (1975) no. 1, p. 1175-1179 / Harvested from Project Euclid
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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.
Publié le : 1975-09-14
Classification:  Conditional distribution,  independence,  substitution,  regular conditional probability,  Wishart,  matrix-variate beta,  62E15,  62H10 
@article{1176343248,
     author = {Perlman, Michael D. and Wichura, Michael J.},
     title = {A Note on Substitution in Conditional Distribution},
     journal = {Ann. Statist.},
     volume = {3},
     number = {1},
     year = {1975},
     pages = { 1175-1179},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343248}
}

Perlman, Michael D.; Wichura, Michael J. A Note on Substitution in Conditional Distribution. Ann. Statist., Tome 3 (1975) no. 1, pp.  1175-1179. http://gdmltest.u-ga.fr/item/1176343248/