An Extension of a Result on the Relationship Between Conditional and Unconditional Independence

P. Pérez Fernández, A. García Nogales

A result by the same authors relating conditional and unconditional independence is generalized. The mentioned result, part of a paper by Nogales and Pérez (2019, to appear in Statistica Neerlandica), uses conditional distribution of a Markov kernel given another (see Nogales (2013, Statistics and Probability Letters)) to obtain a minimal condition which added to a conditional independence implies another conditional independence in some special case. Namely, the conditional independence between some Markov kernels (in fact, the cited Markov kernels are conditional distributions between the concerned random variables) is used to obtain a minimal condition which added to conditional independence of X and Y given Z implies the conditional independence of X and Y given U, provided U is a function of Z.

Keywords: Conditional independence Markov kernels

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