Adjusted empirical likelihood method for the tail index of a heavy-tailed distribution

Yizeng Li, Yongcheng Qi

Research output: Contribution to journalArticle

Abstract

Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a heavy-tailed distribution. It is demonstrated in Lu and Peng (2002) that the empirical likelihood-based confidence intervals perform better than confidence intervals based on normal approximation in terms of the coverage probability. In general, the empirical likelihood method can be hindered by its imprecision in the coverage probability when the sample size is small. This may cause a serious undercoverage issue when we apply the empirical likelihood to the tail index as only a very small portion of observations can be used in the estimation of the tail index. In this paper, we employ an adjusted empirical likelihood method, developed by Chen et al. (2008) and Liu and Chen (2010), to constructing confidence intervals of the tail index so as to achieve a better accuracy. We conduct a simulation study to compare the performance of the adjusted empirical likelihood method and the normal approximation method. Our simulation results indicate that the adjusted empirical likelihood method outperforms other methods in terms of the coverage probability and length of confidence intervals. We also apply the adjusted empirical likelihood method to a real data set.

Original languageEnglish (US)
Pages (from-to)50-58
Number of pages9
JournalStatistics and Probability Letters
Volume152
DOIs
StatePublished - Sep 1 2019

Fingerprint

Tail Index
Heavy-tailed Distribution
Empirical Likelihood
Likelihood Methods
Confidence interval
Coverage Probability
Normal Approximation
Tail index
Empirical likelihood
Heavy-tailed distribution
Imprecision
Nonparametric Methods
Statistical Inference
Approximation Methods
Sample Size
Simulation Study
Statistics

Keywords

  • Adjusted empirical likelihood
  • Coverage probability
  • Empirical likelihood
  • Heavy-tailed distribution
  • Tail index

Cite this

Adjusted empirical likelihood method for the tail index of a heavy-tailed distribution. / Li, Yizeng; Qi, Yongcheng.

In: Statistics and Probability Letters, Vol. 152, 01.09.2019, p. 50-58.

Research output: Contribution to journalArticle

@article{8911a2189de14bbe96d2c6e987fb1620,
title = "Adjusted empirical likelihood method for the tail index of a heavy-tailed distribution",
abstract = "Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a heavy-tailed distribution. It is demonstrated in Lu and Peng (2002) that the empirical likelihood-based confidence intervals perform better than confidence intervals based on normal approximation in terms of the coverage probability. In general, the empirical likelihood method can be hindered by its imprecision in the coverage probability when the sample size is small. This may cause a serious undercoverage issue when we apply the empirical likelihood to the tail index as only a very small portion of observations can be used in the estimation of the tail index. In this paper, we employ an adjusted empirical likelihood method, developed by Chen et al. (2008) and Liu and Chen (2010), to constructing confidence intervals of the tail index so as to achieve a better accuracy. We conduct a simulation study to compare the performance of the adjusted empirical likelihood method and the normal approximation method. Our simulation results indicate that the adjusted empirical likelihood method outperforms other methods in terms of the coverage probability and length of confidence intervals. We also apply the adjusted empirical likelihood method to a real data set.",
keywords = "Adjusted empirical likelihood, Coverage probability, Empirical likelihood, Heavy-tailed distribution, Tail index",
author = "Yizeng Li and Yongcheng Qi",
year = "2019",
month = "9",
day = "1",
doi = "10.1016/j.spl.2019.04.015",
language = "English (US)",
volume = "152",
pages = "50--58",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",

}

TY - JOUR

T1 - Adjusted empirical likelihood method for the tail index of a heavy-tailed distribution

AU - Li, Yizeng

AU - Qi, Yongcheng

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a heavy-tailed distribution. It is demonstrated in Lu and Peng (2002) that the empirical likelihood-based confidence intervals perform better than confidence intervals based on normal approximation in terms of the coverage probability. In general, the empirical likelihood method can be hindered by its imprecision in the coverage probability when the sample size is small. This may cause a serious undercoverage issue when we apply the empirical likelihood to the tail index as only a very small portion of observations can be used in the estimation of the tail index. In this paper, we employ an adjusted empirical likelihood method, developed by Chen et al. (2008) and Liu and Chen (2010), to constructing confidence intervals of the tail index so as to achieve a better accuracy. We conduct a simulation study to compare the performance of the adjusted empirical likelihood method and the normal approximation method. Our simulation results indicate that the adjusted empirical likelihood method outperforms other methods in terms of the coverage probability and length of confidence intervals. We also apply the adjusted empirical likelihood method to a real data set.

AB - Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a heavy-tailed distribution. It is demonstrated in Lu and Peng (2002) that the empirical likelihood-based confidence intervals perform better than confidence intervals based on normal approximation in terms of the coverage probability. In general, the empirical likelihood method can be hindered by its imprecision in the coverage probability when the sample size is small. This may cause a serious undercoverage issue when we apply the empirical likelihood to the tail index as only a very small portion of observations can be used in the estimation of the tail index. In this paper, we employ an adjusted empirical likelihood method, developed by Chen et al. (2008) and Liu and Chen (2010), to constructing confidence intervals of the tail index so as to achieve a better accuracy. We conduct a simulation study to compare the performance of the adjusted empirical likelihood method and the normal approximation method. Our simulation results indicate that the adjusted empirical likelihood method outperforms other methods in terms of the coverage probability and length of confidence intervals. We also apply the adjusted empirical likelihood method to a real data set.

KW - Adjusted empirical likelihood

KW - Coverage probability

KW - Empirical likelihood

KW - Heavy-tailed distribution

KW - Tail index

UR - http://www.scopus.com/inward/record.url?scp=85065311614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065311614&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2019.04.015

DO - 10.1016/j.spl.2019.04.015

M3 - Article

VL - 152

SP - 50

EP - 58

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -