Abstract
The article studies the running maxima \(Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}\) where {Xk,n,k ≥ 1,n ≥ 1} is a double array of φ-subgaussian random variables and {am,j,m ≥ 1,j ≥ 1} is a double array of constants. Asymptotics of the maxima of the double arrays of positive and negative parts of {Ym,j,m ≥ 1,j ≥ 1} are studied, when {Xk,n,k ≥ 1,n ≥ 1} have suitable “exponential-type” tail distributions. The main results are specified for various important particular scenarios and classes of φ-subgaussian random variables.
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Acknowledgements
This research was supported by La Trobe University SEMS CaRE Grant “Asymptotic analysis for point and interval estimation in some statistical models”.
This research includes computations using the Linux computational cluster Gadi of the National Computational Infrastructure (NCI), which is supported by the Australian Government and La Trobe University.
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Dedicated to the memory of Professor Yuri Kozachenko (1940-2020)
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Hayek, N.A., Donhauzer, I., Giuliano, R. et al. Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays. Methodol Comput Appl Probab 24, 1341–1366 (2022). https://doi.org/10.1007/s11009-021-09866-6
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DOI: https://doi.org/10.1007/s11009-021-09866-6