Abstarct: In recent years, the rapid growth of high-dimensional data in fields such as image processing, machine learning, and data mining has introduced new challenges to the development of statistical classification methods. Under such circumstances, the performance of many classical classification techniques, particularly discriminant analysis-baxsed methods, deteriorates considerably due to the instability of covariance matrix estimation and the violation of traditional statistical assumptions. Since the covariance matrix constitutes one of the fundamental components of classification decision rules, the development of stable and efficient estimators for this matrix has become a topic of significant importance. This dissertation addresses the problem of statistical classification in high-dimensional settings through the development and application of shrinkage covariance matrix estimators. In the first part of the study, the classification problem is investigated within the frxamework of the multivariate normal distribution. The Ledoit–Wolf shrinkage estimator is employed as a stable alternative to the conventional sample covariance matrix estimator for constructing discriminant rules. The proposed approach is compared with several well-established classification methods, including Graphical Lasso, cross-validation-baxsed approaches, and Support Vector Machines. The results obtained from simulation studies and real-world datasets demonstrate that the use of shrinkage estimation improves estimation stability and reduces classification error rates, particularly in situations where the number of variables exceeds the number of observations. In the second part, the restrictive assumption of multivariate normality is relaxed by extending the classification frxamework to the broader family of elliptically contoured distributions. To this end, a new shrinkage estimator for the covariance matrix under elliptical distributions is developed and incorporated into the classification procedure. Theoretical investigations, simulation experiments, and real data analyses indicate that the proposed method exhibits desirable numerical stability and provides superior or competitive classification performance compared with existing approaches across a variety of scenarios. Furthermore, the proposed estimator demonstrates lower computational cost and more stable convergence behavior than several competing methods. The findings of this dissertation reveal that appropriately constructed shrinkage estimators can substantially improve the performance of statistical classification procedures in high-dimensional and non-normal settings. Beyond contributing to the theoretical foundations of statistical classification, the proposed methodology offers practical advantages for the analysis of complex multivariate data and provides a foundation for future developments in statistical learning and high-dimensional data analysis.