Calibration of the empirical likelihood method for a vector mean

By Sarah C. Emerson, Art B. Owen. 2009

85 citations recorded by the source corpus.

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 by Chen et al. (2008) 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 smallsample 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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/981e31dfecc33982d14b0a8b9ce239be616d5188

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Citations in the corpus

ADJUSTED EMPIRICAL LIKELIHOOD WITH HIGH-ORDER PRECISION (2010, background): “More recently, Emerson and Owen (2009) discussed the level of adjustment for inference on multivariate population mean.”
A penalized empirical likelihood method in high dimensions (2013, methodology): “An alternative formulation of the EL in such situations (called the adjusted EL) is given by Chen, Variyath and Abraham (2008), which is further refined and studied by Emerson and Owen (2009).”
Empirical likelihood on the full parameter space (2013, background): “For n= 10, the AEL statistic suffers from a boundedness problem [Emerson and Owen (2009)] which may lead to trivial 100% confidence regions or inflated coverage probabilities.”
Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation (2017, background): “The assumption that Θ is an open subset is consistent with Stein (1956) and others but differs from what is described in Cox and Hinkley (1979).”