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Article

Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio

Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada
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Entropy 2018, 20(5), 316; https://doi.org/10.3390/e20050316
Received: 24 February 2018 / Revised: 11 April 2018 / Accepted: 11 April 2018 / Published: 25 April 2018
(This article belongs to the Special Issue Foundations of Statistics)
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. View Full-Text
Keywords: adjusted empirical likelihood; coverage probability; nonparametric; nuisance parameter; Sharpe ratio adjusted empirical likelihood; coverage probability; nonparametric; nuisance parameter; Sharpe ratio
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MDPI and ACS Style

Fu, Y.; Wang, H.; Wong, A. Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio. Entropy 2018, 20, 316. https://doi.org/10.3390/e20050316

AMA Style

Fu Y, Wang H, Wong A. Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio. Entropy. 2018; 20(5):316. https://doi.org/10.3390/e20050316

Chicago/Turabian Style

Fu, Yuejiao, Hangjing Wang, and Augustine Wong. 2018. "Adjusted Empirical Likelihood Method in the Presence of Nuisance Parameters with Application to the Sharpe Ratio" Entropy 20, no. 5: 316. https://doi.org/10.3390/e20050316

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