ABSTRACT
Asymptotic studies of estimators have been well established in statistics. Often the estimators are unique for given models. On one hand, the age-period-cohort models yield multiple estimators, presenting major challenges to the asymptotic studies. On the other hand, if the behavior of each estimator is known, it may potentially provide a clue to understanding and further resolving the identification problem. To study the asymptotics, one needs to focus on one estimator at a time. Hence, a penalty approach is taken to focus on the asymptotics of one specific estimator first, and extend the result later to other estimators. The author provides several lemmas to prepare for the major asymptotic results. He considers the asymptotics of the intrinsic estimator and multiple estimators with a fixed t. The author then considers the asymptotics of the multiple estimators with varying t. In particular, he also discusses constrained estimators, focusing on linear constraints.
