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1999 | 26 | 4 | 437-455
Tytuł artykułu

Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using tools of approximation theory, we evaluate rates of bias convergence for sequences of generalized L-statistics based on i.i.d. samples under mild smoothness conditions on the weight function and simple moment conditions on the score function. Apart from standard methods of weighting, we introduce and analyze L-statistics with possibly random coefficients defined by means of positive linear functionals acting on the weight function.
Rocznik
Tom
26
Numer
4
Strony
437-455
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-02-18
poprawiono
1999-06-16
Twórcy
  • Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, U.S.A.
  • Institute of Mathematics, Polish Academy of Sciences, Chopina 12 , 87-100 Toruń, Poland
Bibliografia
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  • H. A. David (1981), Order Statistics, 2nd ed., Wiley, New York.
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  • H. H. Gonska and R. K. Kovacheva (1994), The second order modulus revisited: remarks, applications, problems, Confer. Sem. Mat. Univ. Bari 257, 1-32.
  • H. H. Gonska and I. Meier (1984), Quantitative theorems on approximation by Bernstein-Stancu operators, Calcolo 21, 317-335.
  • H. H. Gonska and D.-X. Zhou (1995), Local smoothness of functions and Bernstein-Durrmeyer operators, Comput. Math. Appl. 30, No. 3-6 (special issue Concrete Analysis, G. A. Anastassiou (ed.)), 83-101.
  • H. H. Gonska and X.-L. Zhou (1995), The strong converse inequality for the Bernstein-Kantorovich operators, ibid., 103-128.
  • M. Heilmann (1988), $L_p$-saturation of some modified Bernstein operators, J. Approx. Theory 54, 260-273.
  • R. Helmers, P. Janssen and R. Serfling (1990), Berry-Essen and bootstrap results for generalized L-statistics, Scand. J. Statist. 17, 65-77.
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  • H.-B. Knoop and X.-L. Zhou (1992), The lower estimate for linear positive operators, part 1: Constr. Approx. 11 (1995), 53-66, part 2: Results Math. 25 (1994), 300-315.
  • C.-D. Lea and M. L. Puri (1988), Asymptotic properties of linear functions of order statistics, J. Statist. Plann. Inference 18, 203-223.
  • D. H. Mache (1995), A link between Bernstein polynomials and Durrmeyer polynomials with Jacobi weights, in: Approximation Theory VIII, Vol. 1: Approximation and Interpolation, C. K. Chui and L. L. Schumaker (eds.), World Scientific, Singapore, 403-410.
  • V. Maier (1978a), $L_p$ approximation by Kantorovich operators, Anal. Math. 4, 289-295.
  • V. Maier (1978b), The $L_1$ saturation class of the Kantorovich operator, J. Approx. Theory 22, 223-232.
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  • D. M. Mason and G. R. Shorack (1992), Necessary and sufficient conditions for asymptotic normality of L-statistics, ibid. 20, 1779-1804.
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  • R. Paltanea (1998), On an optimal constant in approximation by Bernstein operators, Rend. Circ. Mat. Palermo, to appear.
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Typ dokumentu
Bibliografia
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