×

On functionals of order statistics. (English) Zbl 0484.62063


MSC:

62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Bickel, P.J.: Some contributions to the theory of order statistics. Proc. Fifth Berkeley Symp. Math. Stat. Prob., Vol. 1, 1967. · Zbl 0214.46602
[2] Bickel, P.J., andM.J. Wichura: Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Stat.42, 1971, 1656–1670. · Zbl 0265.60011 · doi:10.1214/aoms/1177693164
[3] Billingsley, P.: Convergence of probability measures. New York 1968. · Zbl 0172.21201
[4] Chandra, M., andN.D. Singpurwalla: The Gini-index, the Lorenz curve, and the total time on test transforms. Inst. f. Management Sci., Washington, preprint, 1978.
[5] Chernoff, H., J.L. Gastwirth, andM.V. Johns Jr.: Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation. Ann. Math. Stat.33, 1967, 52–72. · Zbl 0157.47701 · doi:10.1214/aoms/1177699058
[6] Gänssler, P., andW. Stute: Wahrscheinlichkeitstheorie. Berlin 1977.
[7] Gikhman, I.I., andA.V. Skorokhod: Introduction to the theory of random processes. Philadelphia 1969. · Zbl 0203.49904
[8] Gikhman, I.I., andA.V. Skorokhod: The theory of stochastic processes. Berlin 1974. · Zbl 0132.37902
[9] Goldie, C.: Convergence theorems for empirical Lorenz-curves and their inverses. Adv. Appl. Prob.9, 1977, 765–791. · Zbl 0383.60003 · doi:10.2307/1426700
[10] Govindarajulu, Z.: Asymptotic normality of linear combinations of order statistics. II. Proc. Nat. Acad. Sci.59, 1968, 713–719. · Zbl 0225.62065 · doi:10.1073/pnas.59.3.713
[11] Hecker, H.: A characterization of the asymptotic normality of linear combinations of order statistics from the uniform distribution. Ann. Stat.4, 1975, 1244–1246. · Zbl 0345.62033 · doi:10.1214/aos/1176343656
[12] Hoffman-Jørgenson, J.: The Theory of Analytic Spaces. Aarhus, Series No. 10, 1970.
[13] Moore, D.S.: An elementary proof of asymptotic normality of linear functions of order statistics. Ann. Math. Stat.39, 1968, 263–265. · Zbl 0188.51303 · doi:10.1214/aoms/1177698529
[14] Neuhaus, G.: On weak convergence of stochastic processes with multidimensional time parameter. Ann. Math. Stat.42, 1971, 1285–1295. · Zbl 0222.60013 · doi:10.1214/aoms/1177693241
[15] Parthasarathy, K.R.: Probability measures on metric spaces. New York-London 1967. · Zbl 0153.19101
[16] Pyke, R., andG.R. Shorack: Weak convergence of two-sample empirical process and a new approach to Chernoff-Savage theorems. Ann. Math. Stat.39, 1968, 755–771. · Zbl 0159.48004 · doi:10.1214/aoms/1177698309
[17] Sendler, W.: On statistical inference in concentration measurement. Metrika26, 1979, 109–122. · Zbl 0416.62038 · doi:10.1007/BF01893478
[18] Shorack, G.R.: Functions of order statistics. Ann. Math. Stat.43, 1972, 412–427. · Zbl 0239.62037 · doi:10.1214/aoms/1177692622
[19] Skorokhod, A.V.: Limit theorems for stochastic processes. Theory Prob. Appl.1, 1956, 261–290. · Zbl 0074.33802 · doi:10.1137/1101022
[20] Stigler, S.M.: The asymptotic distribution of the trimmed mean. Ann. Stat.1, 1973, 472–477. · Zbl 0261.62016 · doi:10.1214/aos/1176342412
[21] Wichura, M.: On the construction of almost uniformly convergent random variables with given weakly convergent image laws. Ann. Math. Stat.41, 1970, 284–291. · Zbl 0218.60005 · doi:10.1214/aoms/1177697207
[22] Zwet, W.v.: A strong law for linear functions of order statistics. Ann. Prob.8, 1980, 986–990. · Zbl 0448.60025 · doi:10.1214/aop/1176994626
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.