Fu Yuejiao, Wang Hangjing, Wong Augustine
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada.
Entropy (Basel). 2018 Apr 25;20(5):316. doi: 10.3390/e20050316.
The Sharpe ratio is a widely used risk-adjusted performance measurement in economics and finance. Most of the known statistical inferential methods devoted to the Sharpe ratio are based on the assumption that the data are normally distributed. In this article, without making any distributional assumption on the data, we develop the adjusted empirical likelihood method to obtain inference for a parameter of interest in the presence of nuisance parameters. We show that the log adjusted empirical likelihood ratio statistic is asymptotically distributed as the chi-square distribution. The proposed method is applied to obtain inference for the Sharpe ratio. Simulation results illustrate that the proposed method is comparable to Jobson and Korkie's method (1981) and outperforms the empirical likelihood method when the data are from a symmetric distribution. In addition, when the data are from a skewed distribution, the proposed method significantly outperforms all other existing methods. A real-data example is analyzed to exemplify the application of the proposed method.
夏普比率是经济学和金融学中广泛使用的风险调整后绩效衡量指标。大多数已知的用于夏普比率的统计推断方法都是基于数据呈正态分布这一假设。在本文中，我们在不对数据做任何分布假设的情况下，开发了调整后的经验似然方法，以在存在干扰参数的情况下对感兴趣的参数进行推断。我们表明，对数调整后的经验似然比统计量渐近地服从卡方分布。所提出的方法被应用于对夏普比率进行推断。模拟结果表明，当数据来自对称分布时，所提出的方法与乔布森和科尔基（1981年）的方法相当，并且优于经验似然方法。此外，当数据来自偏态分布时，所提出的方法显著优于所有其他现有方法。通过分析一个实际数据示例来例证所提出方法的应用。
