The article introduces a new method for estimating covariance matrices, which are used in statistical models. The method focuses on selecting the best structure for the covariance matrix, called Toeplitz structure, to improve accuracy and efficiency. By using a special mathematical function, the method can choose the right structure and estimate the matrix at the same time. The researchers found that their method can accurately estimate Toeplitz covariance structures, even in high-dimensional cases. They tested the method with real data and it performed well in practice.