Next Article in Journal
Divergence from, and Convergence to, Uniformity of Probability Density Quantiles
Next Article in Special Issue
Principles of Bayesian Inference Using General Divergence Criteria
Previous Article in Journal
Virtual Network Embedding Based on Graph Entropy
Previous Article in Special Issue
Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(5), 316; https://doi.org/10.3390/e20050316

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
*
Author to whom correspondence should be addressed.
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)
Full-Text   |   PDF [328 KB, uploaded 3 May 2018]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top