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

George Anastassiou; Tomasz Rychlik

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 4, page 437-455
  • ISSN: 1233-7234

Abstract

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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.

How to cite

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Anastassiou, George, and Rychlik, Tomasz. "Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case." Applicationes Mathematicae 26.4 (1999): 437-455. <http://eudml.org/doc/219250>.

@article{Anastassiou1999,
abstract = {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.},
author = {Anastassiou, George, Rychlik, Tomasz},
journal = {Applicationes Mathematicae},
keywords = {Bernstein operator; modulus of smoothness; generalized L-statistic; Kantorovich operator; bias; positive linear operator; random weighting; Bernstein-Durrmeyer operator; K-functional; rate of convergence; K-functionals; positive linear operators},
language = {eng},
number = {4},
pages = {437-455},
title = {Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case},
url = {http://eudml.org/doc/219250},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Anastassiou, George
AU - Rychlik, Tomasz
TI - Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 4
SP - 437
EP - 455
AB - 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.
LA - eng
KW - Bernstein operator; modulus of smoothness; generalized L-statistic; Kantorovich operator; bias; positive linear operator; random weighting; Bernstein-Durrmeyer operator; K-functional; rate of convergence; K-functionals; positive linear operators
UR - http://eudml.org/doc/219250
ER -

References

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