Bounds on coverage probabilities of the empirical likelihood ratio confidence regions

By Min Tsao. 2004

79 citations recorded by the source corpus.

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e413d842c602fee62017b3ddaec34c62cef1e4de

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In Statistics and Probability

Citations in the corpus

Adjusted Empirical Likelihood and its Properties (2008, methodology): “As discussed by Tsao (2004), however, confidence regions computed via the unadjusted EL are by definition confined to be inside the convex hull formed by the observed values, which is not affected by Bartlett correction or by bootstrap calibration.”
A review on empirical likelihood methods for regression (2009, methodology): “Using empirical likelihood for inference on the mean of the response variable when the response is subject to missingness at random was considered in Wang and Rao (2002) for a nonparametric regression model and Wang, Linton and Härdle (2004) for a semiparametric partially linear regression model.”
Effects of data dimension on empirical likelihood (2009, background): “In an earlier study, Tsao (2004) found that, when p is moderately large but fixed, the distribution of `n(µ) has an atom at infinity for a fixed n, namely the probability of `n(µ) = ∞ is non-zero, which reflects the effect of p on the empirical likelihood from another perspective.”
Calibration of the empirical likelihood method for a vector mean (2009, background): “It has been widely noted (see, for example, Owen (2001), Tsao (2004a), or Chen et al. (2008)) that in small samples or high dimensional problems, the asymptotic chi-square calibration of the empirical likelihood ratio statistic produces a test that generally does not achieve the nominal error rate,…”
Penalized empirical likelihood and growing dimensional general estimating equations (2012, background): “We noteadditionally that with r = 2p estimating equations whenp ≥ 30, the optimization of empirical likelihood can be unstable and sometimes may fail, a phenomenon observed by Tsao (2004) and Grend́ar & Judge (2009).”
ADJUSTED EMPIRICAL LIKELIHOOD WITH HIGH-ORDER PRECISION (2010, methodology): “Yet they do not always live up to their promise, particularly for high-dimensional data [Corcoran, Davison and Spady (1995) and Tsao (2004)].”
Empirical likelihood on the full parameter space (2013, background): “To assess its impact on coverage probabilities of empirical likelihood ratio confidence regions, Tsao (2004) investigated bounds on coverage probabilities resulting from the convex hull constraint.”
A penalized empirical likelihood method in high dimensions (2013, background): “However, the most important implication of Theorem 3.2 is that under SRD, the penalization step circumvents the limitation of the standard EL which is known to break down beyond the threshold p≤ n/2, as shown by Tsao (2004).”