Let (\Omega,\cal A,\cal P) stand for a statistical experiment and \cal B,\cal C for some sub- σ-algebras of \cal A with \cal C\subset \cal B . It is shown that for any \cal B -measurable d\in\bigcap_P\in \cal P\,\cal L_2(\Omega,\cal A,P) there exists some d_1\in\bigcap_P\in \cal P\cal L_2(\Omega,\cal A,P) being \cal C -measurable and a UMVU estimator in (\Omega,\cal A,\cal P) and some conditional white noise d_2\in\bigcap_P\in \cal P\,\cal L_2(\Omega,\cal A,P) , i.e.

E_P(d_2\vert \cal C)=0,P\in \cal P , satisfying d=d_1+d_2 , where d_j,j=1,2 , are uniquely determined up to P -zero sets, if and only if \cal C is sufficient and complete for \cal P\vert \cal B and \cal B is optimality robust for \cal P , i.e. any \cal B -measurable d\in\bigcap_P\in \cal P\,\cal L_2(\Omega,\cal A,P) being some UMVU estimator in the restricted statistical experiment (\Omega,\cal B,\cal P\vert \cal B) is already a UMVU estimator in the original statistical experiment (\Omega,\cal A,\cal P) . In particular, the special case \cal B=\cal A characterizes sufficiency and completeness of \cal C for \cal P and the special case \cal B=\cal C optimality robustness and completeness of \cal C for \cal P from a decomposition theoretical point of view. As an application it is shown that a σ-algebra containing a sufficient and complete sub- σ-algebra is optimality robust without being itself in general neither sufficient nor complete.