While the existing literature includes substantial numerical investigations into various shrinkage ridge and Liu estimators, it often lacks a cohesive approach to their construction. This gap signals a need for a unified construction methodology that can provide a clearer framework for understanding and applying Liu estimators in practice. By establishing such a methodology, we aim to simplify the utilization of these estimators and promote their adoption in various statistical applications. This paper will discuss the theoretical underpinnings of shrinkage learners with focus on the seemingly unrelated semiparametric regression model. Through this construction analysis, we ultimately aim to enhance the ongoing discourse in the field of shrinkage learners, offering valuable insights that support researchers and practitioners in choosing suitable techniques for their specific data challenges.

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