Electronic Journal of Statistics

Calibration of the empirical likelihood method for a vector mean

Sarah C. Emerson and Art B. Owen

Full-text: Open access


The empirical likelihood method is a versatile approach for testing hypotheses and constructing confidence regions in a non-parametric setting. For testing the value of a vector mean, the empirical likelihood method offers the benefit of making no distributional assumptions beyond some mild moment conditions. However, in small samples or high dimensions the method is very poorly calibrated, producing tests that generally have a much higher type I error than the nominal level, and it suffers from a limiting convex hull constraint. Methods to address the performance of the empirical likelihood in the vector mean setting have been proposed in a number of papers, including a contribution that suggests supplementing the observed dataset with an artificial data point. We examine the consequences of this approach and describe a limitation of their method that we have discovered in settings when the sample size is relatively small compared with the dimension. We propose a new modification to the extra data approach that involves adding two points and changing the location of the extra points. We explore the benefits that this modification offers, and show that it results in better calibration, particularly in difficult cases. This new approach also results in a small-sample connection between the modified empirical likelihood method and Hotelling’s T-square test. We show that varying the location of the added data points creates a continuum of tests that range from the unmodified empirical likelihood statistic to Hotelling’s T-square statistic.

Article information

Electron. J. Statist., Volume 3 (2009), 1161-1192.

First available in Project Euclid: 1 December 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62H15: Hypothesis testing

Empirical likelihood nonparametric hypothesis testing multivariate hypothesis testing


Emerson, Sarah C.; Owen, Art B. Calibration of the empirical likelihood method for a vector mean. Electron. J. Statist. 3 (2009), 1161--1192. doi:10.1214/09-EJS518. https://projecteuclid.org/euclid.ejs/1259677089

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