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Deviation inequality for Banach-valued orthomartingales

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  • Giraudo, Davide

Abstract

We show a deviation inequality inequalities for multi-indexed martingale We then provide applications to kernel regression for random fields and rates in the law of large numbers for orthomartingale difference random fields.

Suggested Citation

  • Giraudo, Davide, 2024. "Deviation inequality for Banach-valued orthomartingales," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:spapps:v:175:y:2024:i:c:s0304414924000978
    DOI: 10.1016/j.spa.2024.104391
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    References listed on IDEAS

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    1. Mohamed Machkouri, 2007. "Nonparametric Regression Estimation for Random Fields in a Fixed-Design," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 29-47, January.
    2. Volný, Dalibor, 2019. "On limit theorems for fields of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 841-859.
    3. Klicnarová, Jana & Volný, Dalibor & Wang, Yizao, 2016. "Limit theorems for weighted Bernoulli random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1819-1838.
    4. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    5. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.
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