Stair nesting is a type of nesting that leads to very light models. In  this design, the number of treatments is the sum of the number of levels in each factor, instead of being the product of the number of levels in each factor as happens with the usual balanced nesting. In this work, we will present conditions that will allow us to obtain complete sufficient statistics and uniformly minimum variance unbiased estimators (UMVUEs) for the stair nested designs.

uniformly minimum variance unbiased estimator (UMVUE), commutative orthogonal block structure (COBS), stair nested designs.