Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution

Peng, Liang

doi:10.1214/009053604000000328

Cited by 38 publications

(20 citation statements)

References 21 publications

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“…Later, Peng and Qi (2006a) proposed a new calibration method to overcome the undercoverage problem in constructing confidence intervals. Peng (2004) applied the empirical likelihood method to construct the confidence intervals for a mean from a heavy-tailed distribution. Peng and Qi (2006b) employed a data tilting method to construct the confidence intervals (or regions) for the high quantiles of a heavy-tailed distribution.…”

Section: Empirical Likelihood Methodsmentioning

confidence: 99%

Bootstrap and empirical likelihood methods in extremes

2007

Extremes

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One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domain of attraction of an extreme-value distribution and to predict rare events. In recent years, much effort in developing new methodologies has been made by many researchers in this area so as to diminish the impact of the bias in the estimation and achieve some asymptotic optimality in inference problems such as estimating the optimal sample fractions and constructing confidence intervals of various quantities. In particular, bootstrap and empirical likelihood methods, which have been widely used in many areas of statistics, have drawn attention. This paper reviews some novel applications of the bootstrap and the empirical likelihood techniques in extreme-value statistics.

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Section: Empirical Likelihood Methodsmentioning

confidence: 99%

Bootstrap and empirical likelihood methods in extremes

2007

Extremes

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“…As an effective way for interval estimation and goodness‐of‐fit test, the empirical likelihood method has been extended and applied in many different fields such as regression models (Chen & Van Keilegom, 2009), quantile estimation (Chen & Hall, 1993), additive risk models (Lu & Qi, 2004), two‐sample problems (Zhou & Liang, 2005; Cao & Van Keilegom, 2006; Keziou & Leoni‐Aubin, 2008; Ren, 2008), time series models (Hall & Yao, 2003; Chan, Peng & Qi, 2006; Nordman & Lahiri, 2006; Chen & Gao, 2007; Nordman, Sibbertsen & Lahiri, 2007; Guggenberger & Smith, 2008), heavy‐tailed models (Lu & Peng, 2002; Peng, 2004; Peng & Qi, 2006a, b), high dimensional data (Chen, Peng & Qin, 2009), and copulas (Chen, Peng & Zhao, 2009).…”

Section: Introductionmentioning

confidence: 99%

Reduce computation in profile empirical likelihood method

Peng

2011

Can J Statistics

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Since its introduction by Owen in [29,30], the empirical likelihood method has been extensively investigated and widely used to construct confidence regions and to test hypotheses in the literature.For a large class of statistics that can be obtained via solving estimating equations, the empirical likelihood function can be formulated from these estimating equations as proposed by [35]. If only a small part of parameters is of interest, a profile empirical likelihood method has to be employed to construct confidence regions, which could be computationally costly. In this paper we propose a jackknife empirical likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice.

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“…Many authors have developed methods for non‐ and semi‐parametric regression models. Some related works include: Chen & Hall (1993), Kitamura (1997), Chen & Sitter (1999), Peng (2004), Wang et al (2004), Zhu & Xue (2006), Xue & Zhu (2006, 2007a,b), Stute et al (2007), among others. Qin & Zhang (2007) employed an empirical likelihood method to seek a constrained empirical likelihood estimation of the response mean with the assumption that responses are MAR.…”

Section: Introductionmentioning

confidence: 99%

Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random

Xue

2009

Scandinavian J Statistics

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A kernel regression imputation method for missing response data is developed. A class of bias-corrected empirical log-likelihood ratios for the response mean is defined. It is shown that any member of our class of ratios is asymptotically chi-squared, and the corresponding empirical likelihood confidence interval for the response mean is constructed. Our ratios share some of the desired features of the existing methods: they are self-scale invariant and no plug-in estimators for the adjustment factor and asymptotic variance are needed; when estimating the non-parametric function in the model, undersmoothing to ensure root-"n" consistency of the estimator for the parameter is avoided. Since the range of bandwidths contains the optimal bandwidth for estimating the regression function, the existing data-driven algorithm is valid for selecting an optimal bandwidth. We also study the normal approximation-based method. A simulation study is undertaken to compare the empirical likelihood with the normal approximation method in terms of coverage accuracies and average lengths of confidence intervals. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

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Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution

Cited by 38 publications

References 21 publications

Bootstrap and empirical likelihood methods in extremes

Bootstrap and empirical likelihood methods in extremes

Reduce computation in profile empirical likelihood method

Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random

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