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1993-1995 | 22 | 2 | 201-225
Tytuł artykułu

Asymptotic distributions οf linear combinations of order statistics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the asymptotic distributions of linear combinations of order statistics (L-statistics) which can be expressed as differentiable statistical functionals and we obtain Berry-Esseen type bounds and the Edgeworth series for the distribution functions of L-statistics. We also analyze certain saddlepoint approximations for the distribution functions of L-statistics.
Rocznik
Tom
22
Numer
2
Strony
201-225
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-12-31
Twórcy
  • Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • [1] P. J. Bickel, F. Götze, and W. R. van Zwet, The Edgeworth expansion for U-statistics of degree two, Ann. Statist. 14 (1986), 1463-1484.
  • [2] S. Bjerve, Error bounds for linear combinations of order statistics, ibid. 5 (1977), 357-369.
  • [3] N. Bleinstein, Uniform expansions of integrals with stationary points near algebraic singularity, Comm. Pure Appl. Math. 19 (1966), 353-370.
  • [4] D. D. Boos, The differential approach in statistical theory and robust inference, PhD thesis, Florida State University, 1977.
  • [5] D. D. Boos, A differential for L-statistics, Ann. Statist. 7 (1979), 955-959.
  • [6] D. D. Boos and R. J. Serfling, On Berry-Esseen rates for statistical functions, with applications to L-estimates, technical report, Florida State Univ., 1979.
  • [7] H. Chernoff, J. L. Gastwirth, and V. M. Johns Jr., Asymptotic distribution of linear combinations of order statistics with application to estimations, Ann. Math. Statist. 38 (1967), 52-72.
  • [8] H. E. Daniels, Saddlepoint approximations in statistics, ibid. 25 (1954), 631-649.
  • [9] H. E. Daniels, Tail probability approximations, Internat. Statist. Rev. 55 (1987), 37-48.
  • [10] G. Easton and E. Ronchetti, General saddlepoint approximations, J. Amer. Statist. Assoc. 81 (1986), 420-430.
  • [11] R. Helmers, Edgeworth expansions for linear combinations of order statistics with smooth weight functions, Ann. Statist. 8 (1980), 1361-1374.
  • [12] T. Inglot and T. Ledwina, Moderately large deviations and expansions of large deviations for some functionals of weighted empirical process, Ann. Probab., to appear.
  • [13] J. L. Jensen, Uniform saddlepoint approximations, Adv. Appl. Probab. 20 (1988), 622-634.
  • [14] R. Lugannani and S. Rice, Saddlepoint approximations for the distribution of the sum of independent random variables, ibid. 12 (1980), 475-490.
  • [15] N. Reid, Saddlepoint methods and statistical inference, Statist. Sci. 3 (1988), 213-238.
  • [16] R. J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, 1980.
  • [17] G. R. Shorack, Asymptotic normality of linear combinations of order statistic, Ann. Math. Statist. 40 (1969), 2041-2050.
  • [18] G. R. Shorack, Functions of order statistics, ibid. 43 (1972), 412-427.
  • [19] S. M. Stigler, Linear functions of order statistics, ibid. 40 (1969), 770-788.
  • [20] S. M. Stigler, The asymptotic distribution of the trimmed mean, Ann. Statist. 1 (1973), 472-477.
  • [21] S. M. Stigler, Linear functions of order statistics with smooth weight functions, ibid. 2 (1974), 676-693.
  • [22] R. von Mises, On the asymptotic distribution of differentiable statistical functions, Ann. Math. Statist. 18 (1947), 309-348.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22z2p201bwm
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