This study proposes a novel approach for enhancing regression coefficient estimation in single index linear regression models. We introduce the use of the geometric mean of squared error (GMSE) as a criterion for optimizing coefficient estimation. By minimizing the GMSE, our method aims to improve the accuracy and robustness of regression coefficient estimation compared to traditional methods. Through extensive simulations and real data applications, we demonstrate the effectiveness of our proposed approach in accurately estimating regression coefficients, especially in scenarios with noisy or non-linear relationships between variables.

Regression coefficient estimation, Single index linear regression, Geometric mean of squared error

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