Abstract
Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of x and y. Random imputation is used. Empirical likelihood confidence intervals on the differences are constructed.
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Chen, J., Rao, J.N.K., Sitter, R.R. Efficient random imputation for missing data in complex surveys. Statistica Sinica, 10: 1153–1169 (2000)
Chen, J., Rao, J.N.K. Asymptotic normality under two-phase sampling designs. Statistica Sinica, 17: 1047–1064 (2007)
Chen, S.X., Hall, P. Smoothed empirical likelihood confidence intervals for quantiles. Ann. Statist., 21: 1166–1181 (1993)
Chen, Y., Shao, J. Inference with survey data imputed by hot deck when imputed values are nonidentifiable. Statistica Sinica, 9: 361–384 (1999)
Diciccio, T., Hall, P., Romano, J. Empirical likelihood is Bartlett-correctable. Ann. Statist., 19: 1053–1061 (1991)
Hall, P., Martin, M. On the bootstrap and two-sample problems. Austral J. Statist, 30A: 179–192 (1988)
Hartley, H.O., Rao, J.N.K. A new estimation theory for sample surveys. Biometrika, 55: 547–557 (1968)
Jing, B.Y. Two-sample empirical likelihood method. Statistics and Probability Letters, 24: 315–319 (1995)
Little, R.J.A., Rubin, D.B. Statistical analysis with missing data, (2nd edition). John Wiley & Sons, New York, 2002
Owen, A.B. Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75: 237–249 (1988)
Owen, A.B. Empirical likelihood ratio confidence regions. Ann. Statist., 18: 90–120 (1990)
Owen, A.B. Empirical likelihood for linear models. Ann Statist., 19: 1725–1747 (1991)
Owen, A.B. Empirical likelihood. Chapman & Hall, New York, 2001
Qin, J., Lawless, J. Empirical likelihood and general estimating equations. Ann. Statist., 22: 300–325 (1994)
Qin, Y., Zhao, L. Empirical likelihood ratio intervals for the quantile differences of two populations. Chinese Ann. Math., 18A: 687–694 (1997)
Rao, J.N.K. On variance estimation with imputed survey data. J. Amer. Statist. Assoc., 91: 499–520 (1996)
Serfling, R.J. Approximation theorems of mathematical statistics. John Wiley & Sons, New York, 1980
Thomas, D.R, Grunkemeier, G.L. Confidence interval estimation of survival probabilities for censored data. J. Amer. Statist. Assoc., 70: 865–871 (1975)
Wang, Q., Rao, J.N.K. Empirical likelihood-based inference in linear models with missing data. Scand J. Statist., 29: 563–576 (2002)
Wang, Q., Rao, J.N.K. Empirical likelihood-based inference under imputation for missing response data. Ann. Statist., 30: 896–924 (2002)
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Supported by the National Natural Science Foundation of China (No. 10661003) and Natural Science Foundation of Guangxi (No. 0728092).
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Qin, Ys., Qian, Yj. Empirical likelihood confidence intervals for the differences of quantiles with missing data. Acta Math. Appl. Sin. Engl. Ser. 25, 105–116 (2009). https://doi.org/10.1007/s10255-006-6116-0
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DOI: https://doi.org/10.1007/s10255-006-6116-0