Geodesic
Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case
Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 437-455.

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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.
DOI : 10.4064/am-26-4-437-455
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

George Anastassiou 1 ; Tomasz Rychlik 1

1 
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George Anastassiou; Tomasz Rychlik. Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case. Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 437-455. doi : 10.4064/am-26-4-437-455. http://geodesic.mathdoc.fr/articles/10.4064/am-26-4-437-455/

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