Abstract
Empirical likelihood (EL) was first applied to quantiles by Chen and Hall (1993,Ann. Statist.,21, 1166–1181). In this paper, we shall propose an alternative EL approach which is also some kind of the kernel method. It not only eliminates the need to solve nonlinear equations, but also is extremely easy to implement. Confidence intervals derived from the proposed approach are shown, by an nonparametric version of Wilks' theorem, to have the same order of coverage accuracy (order 1/n) as those of Chen and Hall. Numerical results are presented to compare our method with other methods.
Similar content being viewed by others
References
Adimari G. (1998). An empirical likelihood statistic for quantiles,J. Statist. Comput. Simulation,60 (1), 85–95.
Bhattacharya, R. N. and Rao, R. R. (1976).Normal Approximation and Asymptotic Expansions, Wiley, New York.
Chen, S. (1996). Empirical likelihood confidence intervals for nonparametric density estimation,Biometrika,83 (2), 329–341.
Chen, S. (1997). Empirical likelihood-based kernel density estimation,Austral. J. Statist.,39 (1), 47–56.
Chen, S. and Hall, P. (1993). Smoothed empirical likelihood confidence intervals for quantiles,Ann. Statist.,21 (3), 1166–1181.
Chen, S. and Qin, Y. (2000). Empirical likelihood confidence intervals for local linear smoothers,Biometrika,87 (4), 946–953.
Falk, M. (1984). Relative deficiency of kernel type estimators of quantiles,Ann. Statist.,12 (1), 261–268.
Feldman, D. and Tucker, H. G. (1966). Estimation of non-unique quantiles,Ann. Math. Statist.,37 (2), 451–457.
Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional,Biometrika,75 (2), 237–249.
Owen, A. B. (1990). Empirical likelihood ratio confidence regions,Ann. Statist.,18 (1), 90–120.
Owen, A. B. (2001).Empirical Likelihood, Chapman and Hall, London.
Sheather, S. J. and Marron, J. S. (1990). Kernel quantile estimators,J. Amer. Statist. Assoc.,85 (410), 410–416.
Yang, S. S. (1985). A smooth nonparametric estimator of a quantile function,J. Amer. Statist. Assoc.,80 (392), 1004–1011.
Author information
Authors and Affiliations
About this article
Cite this article
Zhou, W., Jing, BY. Adjusted empirical likelihood method for quantiles. Ann Inst Stat Math 55, 689–703 (2003). https://doi.org/10.1007/BF02523389
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02523389