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In this chapter, we introduced a Liu-type (linear unified-type) estimator for the vector of parameters in a linear regression model, when additional linear restrictions on the parameter vector are assumed to hold. After introducing a penalizing function of the squared norm \(\left \lVert d \hat {\beta }-\beta \right \rVert ^{2}\) , a restricted Liu-type estimation (RLTE) method is proposed by minimizing the sum of squared residuals. The property of the new restricted estimator in its superiority over the restricted ordinary least squares estimator (ROLSE) is then theoretically analyzed. Theoretical comparison and real-life data analysis were carried out to evaluate the performance of the RLTE based on mean squared error (MSE) criterion. The application on the real-life data supported the theoretical comparison that showing the superiority of RLTE over OLSE and ROLSE.

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Restricted Liu-Type Regression Estimators in Linear Regression Model

  • 章节

  • 发表日期：

    2026年

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  • Fikri Akdeniz,
  • Esra Akdeniz

摘要

In this chapter, we introduced a Liu-type (linear unified-type) estimator for the vector of parameters in a linear regression model, when additional linear restrictions on the parameter vector are assumed to hold. After introducing a penalizing function of the squared norm \(\left \lVert d \hat {\beta }-\beta \right \rVert ^{2}\) , a restricted Liu-type estimation (RLTE) method is proposed by minimizing the sum of squared residuals. The property of the new restricted estimator in its superiority over the restricted ordinary least squares estimator (ROLSE) is then theoretically analyzed. Theoretical comparison and real-life data analysis were carried out to evaluate the performance of the RLTE based on mean squared error (MSE) criterion. The application on the real-life data supported the theoretical comparison that showing the superiority of RLTE over OLSE and ROLSE.