Abstract
Covariance estimation has widespread applications in various fields such as logistic regression and portfolio optimization. However, in high-dimensional or small-sample scenarios, traditional covariance matrix estimation often encounters the problem of non-invertibility, which severely restricts the performance of related models. This paper presents a novel regularized covariance estimation method aimed at addressing the crucial issue of non-invertible covariance matrices, which has long been a limitation of traditional approaches. The proposed method can ensure the invertibility of the estimated covariance matrix, thereby enhancing numerical stability and reliability. We integrated this method into the analytical solution framework of logistic regression, thereby significantly improving the stability and accuracy of the analytical solution. We apply the proposed method to portfolio return management and demonstrate its effectiveness at improving the quality of optimization solutions for financial applications. Experimental results demonstrate that our method outperforms traditional methods on both logistic regression prediction and portfolio optimization, highlighting its practical value and robustness.