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Statistica Sinica 25 (2015), 1659-1677

LARGE DIMENSIONAL EMPIRICAL LIKELIHOOD
Binbin Chen1, Guangming Pan1, Qing Yang1 and Wang Zhou2
1Nanyang Technological University and 2National University of Singapore

Abstract: The empirical likelihood is a versatile nonparametric approach to testing hypotheses and constructing confidence regions. However it is not clear if Wilks’ Theorem still works in high dimensions. In this paper, by adding two pseudo-observations to the original data set, we prove the asymptotic normality of the log empirical likelihood-ratio statistic when the sample size and the data dimension are comparable. In practice, we suggest using the normalized F(p,n-p) distribution to approximate its distribution. Simulation results show excellent performance of this approximation.

Key words and phrases: Empirical likelihood, large dimensional data.

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