### For REFEREES

 On equalities of BLUEs for a multiple restricted partitioned linear model Keywords:Partitioned linear model, Restricted models, BLUE, Additive decomposition of estimation, Moore-Penrose inverse. Abstract: For the multiple restricted partitioned linear model {\color{blue}${\mathscr{M}}=\{y, X_1$ $\beta_1+\cdots+X_s\beta_s\mid A_1\beta_1=b_1, \cdots, A_s\beta_s=b_s, \Sigma\}$, the relationships between the restricted partitioned linear model ${\mathscr{M}}$ and the corresponding $s$ small restricted linear models ${\mathscr{M}}_i=\{y, X_i\beta_i\mid A_i\beta_i=b_i, \Sigma\},~i=1, \cdots , s$ are studied. The necessary and sufficient conditions for the best linear unbiased estimators $(\mbox{BLUEs})$ under the full restricted model to be the sums of BLUEs under the $s$ small restricted model are derived.} Some statistical properties of the \mbox{BLUEs} are also described.