×

zbMATH — the first resource for mathematics

Confidence tubes for multiple quantile plots via empirical likelihood. (English) Zbl 0957.62038
Summary: The nonparametric empirical likelihood approach is used to obtain simultaneous confidence tubes for multiple quantile plots based on \(k\) independent (possibly right-censored) samples. These tubes are asymptotically distribution free, except when both \(k\geq 3\) and censoring is present. Pointwise versions of the confidence tubes, however, are asymptotically distribution free in all cases. The various confidence tubes are valid under minimal conditions. The proposed methods are applied in three real data examples.

MSC:
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ALY, E.-E. A. A. 1986. Quantile-quantile plots under random censorship. J. Statist. Plann. Inference 15 123 128.Z. · Zbl 0616.62062
[2] BEIRLANT, J. and DEHEUVELS, P. 1990. On the approximation of P-P and Q-Q plot processes by Brownian bridges. Statist. Probab. Lett. 9 241 251. Z. · Zbl 0757.60019
[3] DEHEUVELS, P. and EINMAHL, J. H. J. 1992. Approximations and two-sample tests based on P-P and Q-Q plots of the Kaplan Meier estimators of lifetime distributions. J. Multivariate Anal. 43 200 217. Z. · Zbl 0761.62047
[4] DOKSUM, K. A. 1974. Empirical probability plots and statistical inference for nonlinear models in the two-sample case. Ann. Statist. 2 267 277. Z. · Zbl 0277.62034
[5] DOKSUM, K. A. 1977. Some graphical methods in statistics. A review and some extensions. Statist. Neerlandica 31 53 68. · Zbl 0361.62032
[6] DOKSUM, K. A. and SIEVERS, G. L. 1976. Plotting with confidence: graphical comparisons of two populations. Biometrika 63 421 434. Z. JSTOR: · Zbl 0344.62038
[7] FISHER, N. I. 1983. Graphical methods in nonparametric statistics: a review and annotated bibliography. Internat. Statist. Rev. 51 25 58. Z. JSTOR: · Zbl 0506.62032
[8] FLEMING, T. R. and HARRINGTON, D. P. 1991. Counting Processes and Survival Analysis. Wiley, New York. Z. · Zbl 0727.62096
[9] HOLLANDER, M., MCKEAGUE, I. W. and YANG, J. 1997. Likelihood ratio-based confidence bands for survival functions. J. Amer. Statist. Assoc. 92 215 226. Z. JSTOR: · Zbl 1090.62560
[10] LI, G. 1995. On nonparametric likelihood ratio estimation of survival probabilities for censored data. Statist. Probab. Lett. 25 95 104. Z. · Zbl 0851.62026
[11] LI, G., HOLLANDER, M., MCKEAGUE, I. W. and YANG, J. 1995. Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data. Ann. Statist. 23 628 640. Z. NAIK-NIMBALKAR, U. V. and RAJARSHI, M. B. 1997. Empirical likelihood ratio test for equality of k medians in censored data. Statist. Probab. Lett. 34 267 273. Z. · Zbl 0859.62047
[12] NAIR, V. N. 1978. Graphical Comparisons of Populations in Some Non-linear Models. Ph.D. dissertation, Univ. California, Berkeley. Z.
[13] NAIR, V. N. 1982. Q-Q plots with confidence bands for comparing several populations. Scand. J. Statist. 9 193 200. Z. · Zbl 0503.62006
[14] OWEN, A. 1988. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237 249. Z. JSTOR: · Zbl 0641.62032
[15] OWEN, A. 1990. Empirical likelihood ratio confidence regions. Ann. Statist. 18 90 120. Z. · Zbl 0712.62040
[16] PAULAUSKAS, V. and RACKAUSKAS, A. 1989. Approximation Theory in the Central Limit Theo rem. Exact Results in Banach Spaces. Kluwer, Dordrecht. Z. · Zbl 0715.60023
[17] PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T. and FLANNERY, B. P. 1992. Numerical Recipes in C, 2nd ed. Cambridge Univ. Press. Z. · Zbl 0778.65003
[18] SHORACK, G. R. and WELLNER, J. A. 1986. Empirical Processes with Applications to Statistics. Wiley, New York. Z. · Zbl 1170.62365
[19] SWITZER, P. 1976. Confidence procedures for two-sample problems. Biometrika 63 13 25. Z. JSTOR: · Zbl 0335.62035
[20] THOMAS, D. R. and GRUNKEMEIER, G. L. 1975. Confidence interval estimation of survival probabilities for censored data. J. Amer. Statist. Assoc. 70 865 871. JSTOR: · Zbl 0331.62028
[21] EINDHOVEN UNIVERSITY OF TECHNOLOGY TALLAHASSEE, FLORIDA 32306-4330 P.O. BOX 513 E-MAIL: mckeague@stat.fsu.edu 5600 MB EINDHOVEN THE NETHERLANDS E-MAIL: einmahl@win.tue.nl
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.