In the presence of nonnormally distributed asset returns, optimal portfolio selection techniques require estimates for variance-covariance parameters, along with estimates for higher-order moments and comoments of the return distribution. This is a formidable challenge that severely exacerbates the dimensionality problem already present with meanvariance analysis. In this thesis, we give a comprehensive review of sample estimator, structured and shrinkage estimators for higher-order moments and comoments of asset returns. By various simulation studies in R, we will compare the performance of these approaches in the optimal portfolio selection within high frequency data and point out advantages and disadvantages for each approach. The main target is to use these approaches to analyze the real financial data, i.e., S&P 500 daily index and asset returns. From the results of numerical simulation, we find that the single-factor approach and the estimator shrunk toward the single factor estimator outperform their constant correlation counterparts in high frequency data. However, the sample estimator also performs well in this environment.