Consider the linear regression model:$$y=\beta_{0}+\beta_{1}x+u$$
The OLS estimators minimze the squared sum of residuals. By the Gauss-Markov theorem, OLS estimators give the lowest variance of estimates in the class of unbiased estimators. However, we also know that estimators such as Ridge estimators exploit the Bias-Variance tradeoff and are able to achieve higher efficiency. Is there an estimator that would maximizes the t-value of a test of the null:$$H_{0}:\beta_{1}=0$$ or the ratio$$\frac{\hat{\beta}}{SE(\hat{\beta})}$$