Probability inequalities and limit theorems for generalized L-statistics. (English. Russian original) Zbl 1052.60015

Baklanov, E. A.; Borisov, I. S.

Lith. Math. J. 43, No. 2, 125-140 (2003); translation from Liet. Mat. Rink 43, No. 2, 149-168 (2003).

This paper extends the authors’ previous work [Sib. Mat. J. 42, 217–231 (2001); translation from Sib. Mat. Zh. 42, 258–274 (2001; Zbl 0986.60014). Exponential bounds are obtained for the tails of the distributions of generalized \(L\)-statistics based on a sample from an exponential distribution. The asymptotic normality of generalized \(L\)-statistics based on a sample from a uniform distribution is investigated along with the asymptotic normality of \(L\)-statistics with decomposed kernels. In the latter case no restrictions are placed on the distribution type of the sample.

Reviewer: Neville Weber (Sydney)

MSC:

60F05	Central limit and other weak theorems
60E15	Inequalities; stochastic orderings

Keywords:

L-statistics; asymptotic normality; exponential upper bounds; order statistics

Citations:

Zbl 0986.60014