On the Bahadur Representation of Quantiles for a Sample from ρ*-Mixing Structure Population
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Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20–618 Lublin, Poland
Publication date: 2022-07-01
Corresponding author
Dagmara Dudek
Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20–618 Lublin, Poland
Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20–618 Lublin, Poland
Adv. Sci. Technol. Res. J. 2022; 16(3):316–330
KEYWORDS
quantilesbahadur representationasymptotic normalityberry-esseen boundsimulationρ*-mixing random variables
TOPICS
ABSTRACT
In this paper, we establish the strong consistency and the Bahadur representation of sample quantiles for ρ*-mixing random variables. Additionally, the asymptotic normality and the Berry-Esseen bound of sample quantiles for ρ*-mixing random variables are presented. Additionally, we provide the rate of convergence of sample quantiles to population counterparts. Moreover, numerical simulation is presented to ilustrate and verify obtained results.
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