Probability inequalities and limit theorems for generalized L-statistics (Q1881793)

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.