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Large deviations for L-statistics

Statistics & Decisions, 2007
The purpose of this paper is to establish a functional large deviations principle (LDP) for L-statistics under some new tail conditions. The method is based on Sanov's theorem and on basic tools of large deviations theory. Our study includes a full treatment of the case of the uniform law and an example in which the rate function can be calculated very
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Probabilities of large deviations for L-statistics

Lithuanian Mathematical Journal, 1991
See the review in Zbl 0706.62015.
Bentkus, V., Zitikis, R.
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A note on adaptive l-statistics

Communications in Statistics - Theory and Methods, 1982
The purpose of this note is to give a simple demonstration of the apparently widely-known principle that, under suitable conditions (primarily of a symmetry nature) an adaptive L-sta-tistic has the same asymptotic distribution as a non-adaptive L-statistic.
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Bootstrapping for generalized l-statistics

Communications in Statistics - Theory and Methods, 1989
Serfling (1984) introduced a class of generalized L-statistics containing many different types of statistics. For a generalized L-statistic Tn, we establish a bootstrap representation for the bootstrap statistic —Tn, which shows that —Tn can be approximated by the difference between a U-statistic and its bootstrap analog.
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Probability Inequalities and Limit Theorems for Generalized L-Statistics

Lithuanian Mathematical Journal, 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.
Baklanov, E. A., Borisov, I. S.
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A Glivenko-Cantelli Theorem and Strong Laws for L-Statistics

Journal of Theoretical Probability, 1998
Consider the Marcinkiewicz-Zygmund strong law (MZSLLN) which states the almost sure convergence of \(n^{-1}\sum^n_{i=1} X_i=c+o (n^{(1-p)/p})\) a.s. as \(n\to\infty\), for \(\{X_i, i\geq 1\}\) i.i.d.
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An exact bootstrap for variance of finite-population L-statistic

Lithuanian Mathematical Journal, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An L-statistic approach to a test of exponentiality against IFR alternatives

Journal of Statistical Planning and Inference, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitra, Murari, Anis, M. Z.
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On the exact sampling distribution of L-statistics [PDF]

open access: possible, 2003
This paper shows that linear functions of order statistics (L-statistics) based on random samples have a Fundamental Skew distribution (Arellano-Valle Genton, 2003). The paper also examines the exact distribution of L-statistics when the sampled population is Skew Normal. Exact distributions of L-statistics from normal samples easily follows as special
Corrado Crocetta, Nicola Loperfido
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Asymptotic Properties of Exponentiality Tests Based on L-Statistics

Acta Applicandae Mathematicae, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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