Asymptotic Properties of the Deviation Between Order Statistics and p-Quantile

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 1; pp. 8 - 14
• Main Authors: Miao, Yu, Chen, Ying-Xia, Xu, Shou-Fang
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.01.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Asymptotic properties; Bahadur's asymptotic efficiency; Deviation; Exact sciences and technology; General topics; Large deviation; Limit theorems; Mathematics; Moderate deviation; Nonparametric inference; Order statistics; p-quantile; Probability; Probability and statistics; Probability theory and stochastic processes; Sampling theory, sample surveys; Sciences and techniques of general use; Statistics; Studies; Bahadur efficiency; Sample size; 60F10; Asymptotic behavior; Order statistic; Non parametric estimation; Statistical estimation; Asymptotic efficiency; p-quantile; Order statistics; Large deviation; Statistical method; Sampling theory; Moderate deviation; Bahadur's asymptotic efficiency; Distribution function; 62G30; Sample survey; Quantile
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920903350523

We discuss the asymptotic properties of the deviation between order statistics and p-quantile of an independently and identically distributed sample of size n. The large and moderate deviation principle and Bahadur's asymptotic efficiency of the deviation X (k)  − ξ p are obtained under some weak conditions.