We apply the procedure of Lee et al. to the problem of performing inference on the signal-noise ratio of the asset which displays maximum sample Sharpe ratio over a set of possibly correlated assets. We find a multivariate analogue of the commonly used approximate standard error of the Sharpe ratio to use in this conditional estimation procedure. We also consider several alternative procedures, including the simple Bonferroni correction for multiple hypothesis testing, which we fix for the case of positive common correlation among assets, the chi-bar square test against one-sided alternatives, Follman's test, and Hansen's asymptotic adjustments. Testing indicates the conditional inference procedure achieves nominal type I rate, and does not appear to suffer from non-normality of returns. The conditional estimation test has low power under the alternative where there is little spread in the signal-noise ratios of the assets, and high power under the alternative where a single asset has high signal-noise ratio. Unlike the alternative procedures, it appears to enjoy rejection probabilities monotonic in the signal-noise ratio of the selected asset, and actually maintains near-nominal rejection rates under the conditional null.

翻译：本文将Lee等人提出的方法应用于对一组可能相关的资产中表现出最大样本夏普比率的资产进行信号噪声比推断的问题。我们找到了常用夏普比率近似标准误的多变量模拟形式，以用于此条件估计过程。我们还考虑了多种替代方法，包括针对多重假设检验的简单Bonferroni校正（我们针对资产间存在正共同相关性的情况进行了修正）、针对单侧备择假设的卡方柱检验、Follman检验以及Hansen的渐近调整。测试结果表明，条件推断方法达到了名义I类错误率，且似乎未受到收益非正态性的影响。在备择假设下，当资产的信号噪声比差异较小时，条件估计检验的效力较低；而当单一资产具有高信号噪声比时，其效力较高。与其他替代方法不同，该方法在选定资产的信号噪声比方面表现出单调的拒绝概率特性，并且在条件零假设下实际保持了接近名义水平的拒绝率。