當市場上存在優異績效的基金時，我們該如何去搜尋它的存在，這是眾多的投資人與經濟學家心中的疑惑。然而，不論是誰想以何種方法去檢驗其猜想，一旦試圖以複數個虛無假設，逐步驗證各檔基金的績效，此人終將面臨一道難以跨越的高牆，也就是多重檢定問題。在廣大的基金市場中，多重檢定問題會隨著樣本數的擴大而顯著地惡化，使得找出的多數標的充斥著錯誤的發現，使得該基金並非優異基金，卻被認證是績效出色的優質基金，影響整體判斷結果的正確性。為了嚴謹地搜尋目標標的，同時控制好錯誤發現的可能，我們需要透過一系列的調整，適度平衡提升檢定力與控制錯誤發現率的兩難。調整手段包括限制基金的存續期間、運用機器學習彌補基金資料的缺失、使用wild bootstrap建立貼近母體的樣本分配以及利用Benjamini and Hochberg演算法，將錯誤控制在一定的範圍。最終，我們才能把真正具有顯著正報酬的基金，從廣大的基金市場中挖掘出來。研究結果總計有138檔基金被至少一種模型給認定為優異基金，而依據模型挑選的基金組合中，最高的年化報酬率高達9.76%，已超越美股大盤的報酬率。

When there are funds with excellent performance in the market, how to search for their existence is the doubt in the minds of most investors and economists. However, no matter what method is used to test, as long as people try to gradually verify the performance of each fund with multiple null hypotheses, they will face a difficult problem needed to overcome, that is, the problem of multiple testing. In the vast fund market, the problem of multiple testing will be significantly worsened with the expansion of the sample size. Therefore, most of the targets found in the process are full of false discoveries, which means that the fund is not an excellent one but is sometimes certified as a fund with good performance, affecting the correctness of the overall testing result. With an aim of rigorously searching for the wanted target while controlling the possibility of false discovery, we need to make a series of adjustments to moderately balance the tradeoff of improving the testing power and controlling the false discovery rate. First, limit the duration of the fund. Next, use machine learning to make up for the lack of fund data. Then, use wild bootstrap to establish a sample distribution close to the matrix. Finally, employ Benjamini and Hochberg procedure to control the occurrence of errors. Eventually, we can discover funds that really have significantly positive returns from the vast fund market. A total of 138 funds has been identified as excellent funds by at least one model, and the highest internal rate of return among all portfolios is as high as 9.76%, surpassing the returns of the US market portfolio.

莊惠菁、管中閔 (2020)，「共同基金卓越績效的認定與評估： 新逐步檢定法的應用」，《證券市場發展季刊》，第 32 卷第 1 期，1-31。
Benjamini, Y., and Y. Hochberg. 1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological) 57:289–300.
Fama, E. F., and K. R. French. 2010. Luck versus skill in the cross-section of mutual fund returns. Journal of Finance 65:1915–47.
Giglio, S., and D. Xiu. 2021. Asset pricing with omitted factors. Journal of Political Economy 129:1947–90.
Giglio, S., Y. Liao, and D. Xiu. 2021. Thousands of Alpha Tests. Review of Financial Studies 34:3456–96.
Hansen, P. 2005. A test for superior predictive ability. Journal of Business and Economic Statistics 23:365–80.
Harvey, C. R., and Y. Liu. 2020. False (and missed) discoveries in financial economics. Journal of Finance 75:2503–53.
Harvey, C. R., and Y. Liu. 2022. Luck versus Skill in the Cross Section of Mutual Fund Returns: Reexamining the Evidence. Journal of Finance 77:1921–66.
Hsu, P. H., Y. C. Hsu, and C. M. Kuan. 2010. Testing the predictive ability of technical analysis using a new stepwise test without data-snooping bias. Journal of Empirical Finance 17:471–84.
Roback, P. J., and R. A. Askins. 2005. Judicious use of multiple hypothesis tests. Conservation Biology 19:261–67.
Romano, J. P., and M. Wolf. 2005. Stepwise multiple testing as formalized data Snooping. Econometrica 73:1237–82.
White, H. 2000. A reality check for data snooping. Econometrica 68:1097–126.