On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications

DOI10.1016/j.spa.2002.10.001zbMath1076.62066OpenAlexW2051268078MaRDI QIDQ2485756

Bernard Bercu

Publication date: 5 August 2005

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

Full work available at URL: https://doi.org/10.1016/j.spa.2002.10.001

zbMATH Keywords

moment estimatorsmartingale transformsASCLT

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Martingales with discrete parameter (60G42) Point estimation (62F10) Exact distribution theory in statistics (62E15) Strong limit theorems (60F15)

Related Items (18)

Large deviation principle for additive functionals of semi-Markov processes ⋮ Semiparametric regression estimation for longitudinal data in models with martingale difference error's structure ⋮ An almost sure limit theorem for the maxima of smooth stationary Gaussian processes ⋮ MODERATE DEVIATIONS FOR THE DURBIN-WATSON STATISTIC ASSOCIATED TO THE STABLE p-ORDER AUTOREGRESSIVE PROCESS ⋮ Toward optimal multistep forecasts in non-stationary autoregressions ⋮ Further results on the \(h\)-test of Durbin for stable autoregressive processes ⋮ A martingale approach for the elephant random walk ⋮ On the almost sure central limit theorem for ARX processes in adaptive tracking ⋮ Weighted Limit Theorems for Continuous-Time Vector Martingales with Explosive and Mixed Growth ⋮ Large Deviations via Almost Sure CLT for Functionals of Markov Processes ⋮ A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error's structure ⋮ Théorèmes limites avec poids pour les martingales vectorielles à temps continu ⋮ Stochastic approximation algorithms for superquantiles estimation ⋮ On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications ⋮ On the multi-dimensional elephant random walk ⋮ A martingale approach for Pólya urn processes ⋮ On the almost sure central limit theorem for the elephant random walk ⋮ Further results on the minimal random walk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the almost sure central limit theorem
• Adaptive prediction by least squares predictors in stochastic regression models with applications to time series
• On the convergence of generalized moments in almost sure central limit theorem
• Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters
• A universal result in almost sure central limit theory.
• Théorèmes limites avec poids pour les martingales vectorielles
• On Almost Sure Limit Theorems
• INVARIANCE PRINCIPLES WITH LOGARITHMIC AVERAGING FOR MARTINGALES
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Adaptive control of parametric nonlinear autoregressive models via a new martingale approach
• Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems
• On large deviations in the Gaussian autoregressive process: Stable, unstable and explosive cases

This page was built for publication: On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications