The Bahadur representation of sample quantiles for φ-mixing random variables and its application. Issue 2 (4th March 2021)

• Record Type: Journal Article
• Authors: Wu, Yi; Yu, Wei; Wang, Xuejun
• Is Part Of: Statistics. Volume 55:Issue 2(2021)
• Page Start: 426
• Page End: 444
• Publication Date: 2021-03-04
• Subjects: Bahadur representation -- sample quantile -- φ-mixing random variables -- asymptotic normality -- Berry–Esséen bound -- real data analysis; 62G05 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1923713
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : In this paper, the Bahadur representation of sample quantiles for φ -mixing random variables is investigated without any restriction on the decaying rate of mixing coefficients. As an application, we further investigate the asymptotic normality and the Berry–Esséen bound of sample quantiles for φ -mixing random variables under some general conditions. It is shown that the rate of normal approximation is O ( n − 1 / 6 + κ ) for any 0 < κ < 1 / 6 if the mixing coefficients satisfy φ ( n ) = O ( n − β ) for some β ≥ 3 / 2 or O ( n − 1 / 4 + ρ ) for any 0 < ρ < 1 / 4 if the mixing coefficients can decay exponentially. Furthermore, a real data analysis is presented.