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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
 
 
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Dagmara Dudek   

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
 
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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.