Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio
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 assum...
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| Format: | Article |
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MDPI AG
2018-04-01
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| Online Access: | http://www.mdpi.com/1099-4300/20/5/316 |
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| author | Yuejiao Fu Hangjing Wang Augustine Wong |
| author_facet | Yuejiao Fu Hangjing Wang Augustine Wong |
| author_sort | Yuejiao Fu |
| collection | DOAJ |
| description | 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. |
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| id | doaj.art-b9e9fcace60e4ab0861eb55813da0d42 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:40:06Z |
| publishDate | 2018-04-01 |
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| spelling | doaj.art-b9e9fcace60e4ab0861eb55813da0d422022-12-22T04:21:17ZengMDPI AGEntropy1099-43002018-04-0120531610.3390/e20050316e20050316Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe RatioYuejiao Fu0Hangjing Wang1Augustine Wong2Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaDepartment of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaDepartment of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaThe 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.http://www.mdpi.com/1099-4300/20/5/316adjusted empirical likelihoodcoverage probabilitynonparametricnuisance parameterSharpe ratio |
| spellingShingle | Yuejiao Fu Hangjing Wang Augustine Wong Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio Entropy adjusted empirical likelihood coverage probability nonparametric nuisance parameter Sharpe ratio |
| title | Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio |
| title_full | Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio |
| title_fullStr | Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio |
| title_full_unstemmed | Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio |
| title_short | Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio |
| title_sort | adjusted empirical likelihood method in the presence of nuisance parameters with application to the sharpe ratio |
| topic | adjusted empirical likelihood coverage probability nonparametric nuisance parameter Sharpe ratio |
| url | http://www.mdpi.com/1099-4300/20/5/316 |
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