# 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

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topAnastassiou, 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 -

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