Let X be a sample obtained using the stratified simple random sampling plan described previously.

(i) For each h, let Z_h be the vector of the ordered values of the sample in stratum h. Then (Z₁, ..., Z_H) is sufficient and complete for θ ∈ Θ.

(ii) For any estimable function of θ, its unique UMVUE is the unbiased estimator g(X) that is symmetric in its first n₁arguments, symmetric in its second n₂ arguments,..., and symmetric in its last n_H arguments.