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.