Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process

DOI10.1017/jpr.2022.134arXiv2107.07965OpenAlexW3186902377MaRDI QIDQ6148876

Xiequan Fan, Qui-Man Shao

Publication date: 12 January 2024

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.07965

zbMATH Keywords

Berry-Esseen boundsoffspring meanself-normalized processesLotka-Nagaev estimator

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Parametric hypothesis testing (62F03) Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Cites Work

• Weak convergence results for multiple generations of a branching process
• Identification of multitype branching processes
• Exponential inequalities for self-normalized martingales with applications
• Large deviation rates for branching processes. I: Single type case
• Harmonic moments and large deviation rates for supercritical branching processes
• Self-normalized Cramér-type large deviations for independent random variables.
• Berry-Esseen bounds for self-normalized martingales
• Exact rates of convergence in some martingale central limit theorems
• Local limit theory and large deviations for supercritical branching processes.
• Self-normalized Cramér type moderate deviations for stationary sequences and applications
• Self-normalized Cramér type moderate deviations for martingales
• On large deviation rates for sums associated with Galton‒Watson processes
• Self-Normalized Processes
• Self-normalized large deviation for supercritical branching processes
• On Estimating the Expected Number of Direct Descendants of a Particle in a Branching Process

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