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Limit behaviors of the deviation between the sample quantiles and the quantile

Xu Shoufang (Department of Mathematics, Xinxiang University, Henan Province, China)
Miao Yu (College of Mathematics and Information Science, Henan Normal University, Henan Province, China)

In this article, we discuss the limit behaviors for the deviation between the sample p-quantile ξˆnp and the p-quantile ξp by sampling from a sequence of independent and identically distributed samples of size n. The moderate deviation, large deviation and Bahadur asymptotic efficiency for (ξˆpn−ξp) are established under some weak conditions.

Keywords: p-quantile, sample p-quantile, large deviation, moderate deviation, Bahadur asymptotic efficiency