Research output: Contribution to conference › Abstract › peer-review
Some recent results on probabilities of large and moderate deviations for L-statistics. / Gribkova, Nadezhda .
2020. 27-33 Abstract from XXXVI International Seminar on Stability Problems for Stochastic Models, Petrozavodsk, Russian Federation.Research output: Contribution to conference › Abstract › peer-review
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TY - CONF
T1 - Some recent results on probabilities of large and moderate deviations for L-statistics
AU - Gribkova, Nadezhda
N1 - Conference code: XXXVI
PY - 2020/5/25
Y1 - 2020/5/25
N2 - The class of L-statistics is one of the most commonly used classes in statisticalinferences. We refer to monographs [5], [11], [12], [14] for the introduction to the theory of L-statistics. A survey on some modern applications of them in the economy and theory of actuarial risks can be found in [7]. There is an extensive literature on asymptotic properties of L-statistics, but its part concerning the large deviations is not so vast. We can mention a few of highly sharp results on this topic for L-statistics with smooth weight functions established in [13], [2], [1]. As to the trimmed L-statistics, the rst { and up to the recent time the single { result on probabilities of large deviations was obtained in [4], but under some strict and unnatural conditions.Recently, the latter result was strengthened in [10], where a dierent approach than in [4] was proposed and implemented. In this note we present some of our recent results established in [8]-[9]. To conclude this short introduction, we want to mention a paper[3], and an interesting article [6], in which a general delta method in the theory of Cherno's type large deviations was proposed and illustrated by many examples including Mestimators and L-statistics.
AB - The class of L-statistics is one of the most commonly used classes in statisticalinferences. We refer to monographs [5], [11], [12], [14] for the introduction to the theory of L-statistics. A survey on some modern applications of them in the economy and theory of actuarial risks can be found in [7]. There is an extensive literature on asymptotic properties of L-statistics, but its part concerning the large deviations is not so vast. We can mention a few of highly sharp results on this topic for L-statistics with smooth weight functions established in [13], [2], [1]. As to the trimmed L-statistics, the rst { and up to the recent time the single { result on probabilities of large deviations was obtained in [4], but under some strict and unnatural conditions.Recently, the latter result was strengthened in [10], where a dierent approach than in [4] was proposed and implemented. In this note we present some of our recent results established in [8]-[9]. To conclude this short introduction, we want to mention a paper[3], and an interesting article [6], in which a general delta method in the theory of Cherno's type large deviations was proposed and illustrated by many examples including Mestimators and L-statistics.
M3 - Abstract
SP - 27
EP - 33
Y2 - 22 June 2020 through 26 June 2020
ER -
ID: 86575331