Equalities of various estimators in the general growth curve model and the restricted growth curve model

•We show the equalities for the OLSE, WLSE and BLUE by rank method.•We study the equalities for various estimators of some parametric functions.•We derive some relationships of estimators between different growth curve models.

We show some equalities for three estimators: (1) the ordinary least-squares estimators (OLSE), (2) the weighted least-squares estimators (WLSE), (3) the best linear unbiased estimator (BLUE) under the general growth curve model (A)μ1={Y,X1ΘX2,σ2(Σ2⊗Σ1)}, and the restricted growth curve model (B)μ2={Y,X1ΘX2|A1Θ=B1,ΘA2=B2,σ2(Σ2⊗Σ1)}, respectively.