Penalised, post-pretest, and post-shrinkage strategies in nonlinear growth models

In nonlinear growth models, we considered the parameter estimation under subspace information for low-dimensional and high-dimensional data. We proposed novel estimators based on pretest and shrinkage strategies to improve the estimation efficiency and to establish asymptotic properties. We used simulation studies and a real data example to confirm the theoretical results. We also applied two well-known penalised methods—least absolute shrinkage and selection operator (LASSO) and adaptive LASSO (aLASSO)—for the dimensional reduction of the predictor variables. The results demonstrated that the pretest and shrinkage estimation strategies performed well in parameter estimations when the subspace information was incorrect for both low- and high-dimensional regimes.