Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains.

DOI10.1016/S0304-4149(00)00025-9zbMath1045.60030MaRDI QIDQ1877531

Rachid Senoussi

Publication date: 7 September 2004

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Markov chainautoregressive modelkernel estimatoriterated logarithm lawcontrolled model

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05) Strong limit theorems (60F15)

Related Items (4)

Revisiting the estimation of the error density in functional autoregressive models ⋮ Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models ⋮ Change detection for uncertain autoregressive dynamic models through nonparametric estimation ⋮ Uniform law of large numbers and consistency of estimators for Harris diffusions

Cites Work

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• Sur la loi des grands nombres pour les martingales vectorielles et l'estimateur des moindres carrés d'un modèle de régression. (On the law of large numbers for vectorial martingales and least square estimators of a regression model)
• The consistency of automatic kernel density estimates
• Strong consistency and rates for recursive probability density estimators of stationary processes
• Strong uniform consistency of nonparametric regression function estimates
• A law of the logarithm for kernel density estimators
• A strong convergence theorem for Banach space valued random variables
• Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments
• Laws of the iterated logarithm for nonparametric density estimators
• Weak and strong uniform consistency of kernel regression estimates
• The Law of Large Numbers for $D[0,1$-Valued Random Variables]

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