There is a great deal of misinformation and out-of-date information on this site. Many of the references in this discussion and elsewhere have serious research flaws.
The Michaud efficient frontier was invented and patented by Robert Michaud and Richard Michaud, U.S. patent # 6,003,018. The alternatives discussed here are not patented nor in many cases refereed.
To answer the original question, Monte Carlo simulation tests are the standard method in modern statistics used to determine the superiority of one statistical procedure over another. Such a study was used to prove that Michaud optimization is superior to MVO. These are mathematical proofs. There is no doubt of the result. But if you need reassurance you can listen to the world’s greatest authority on portfolio optimization, Harry Markowitz, who has said in print: Michaud optimization beats Markowitz optimization.
The simulation tests for Michaud vs. MVO are published in Michaud (1998, Harvard, Chs. 6 and 9) and Michaud and Michaud (2008, Oxford Chs. 6 and 9). The tests were reproduced in Markowitz and Usmen (2003, Journal Of Investment Management). It is important to note that simulation tests are far superior to back tests. A back test proves absolutely nothing. It only tells you what happened during some time period. A different time period may have very different results.
The Markowitz-Usmen tests took for granted that the resampling process we introduced (note: this is not the Morningstar Encorr procedure), is superior to MVO. What Markowitz and Usmen wanted to prove is whether better information beats a better optimizer? They tested MVO and better information against Michaud with much less information. They performed 30 tests and found that their superior information never beat the superior optimizer.
People who have played with Michaud optimization have noted features about the resampled optimizer that are different from MVO. In almost all cases these anomalies are actually very consistent with real investor behavior once properly understood.
I recommend visiting www.newfrontieradvisors.com for much more information on the procedure, various tests and many extensions of the resampling procedure, rejoinders to flawed studies and ideas, and how extensively it is being used around the world in practice today. Many billions of dollars are being managed with Michaud optimization globally. Michaud optimization remains the only portfolio optimizer with a rigorous mathematical proof of investment effectiveness in the world today.