UC Santa Barbara

Statistical analysis in high-dimensional settings faces challenges, as illustrated by Stein’s paradox which questions the effectiveness of traditional estimators. In this study, classical methods like the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) are reinterpreted in high-dimensional contexts. First, we analyze the convergence rates of the James-Stein estimator for principal components. Second, a novel regularized estimator for principal components is proposed, demonstrating superior performance in certain scenarios. Finally, the potential applicability of these advanced estimators in finance, particularly in portfolio optimization and asset pricing, is explored. Overall, our research merges classical statistical paradigms with new methodologies, offering significant insights for various fields.