Traditional portfolio optimization often overlooks estimation risk, which mainly stems from uncertainty in expected asset returns rather than their variances and covariances. The global minimum variance portfolio is suggested as a better alternative, as it doesn't require estimating expected returns, reducing the impact of estimation errors. However, in practical scenarios, investors may prefer a local minimum variance portfolio to minimize return variance while meeting specific constraints. The study presents hypothesis tests for both types of portfolios and analyzes the distribution of estimated portfolio weights and expected returns.