Recursive estimators for stationary, strong mixing processes - a representation theorem and asymptotic distributions

DOI10.1016/0304-4149(89)90088-4zbMath0697.62079OpenAlexW2064020296MaRDI QIDQ911200

Ulla Holst, Jan-Eric Englund, David Ruppert

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0304-4149(89)90088-4

zbMATH Keywords

stationary processesrecursive estimationdependent strong mixing sequencesgeneralizations of the Robbins-Monro processlimit theorems for sumsrecursive M-estimators of location and scalesums of possibly dependent random variables

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Nonparametric estimation (62G05) Stochastic approximation (62L20)

Related Items

Methods for recursive robust estimation of AR parameters ⋮ Truncated stochastic approximation with moving bounds: convergence ⋮ RECURSIVE ESTIMATION IN SWITCHING AUTOREGRESSIONS WITH A MARKOV REGIME ⋮ Recursive parameter estimation: convergence ⋮ Efficient on-line estimation of autoregressive parameters ⋮ Selecting an adaptive sequence for computing recursive M-estimators in multivariate linear regression models ⋮ On the recursive parameter estimation in the general discrete time statistical model ⋮ Rate of convergence of truncated stochastic approximation procedures with moving bounds

Cites Work

• M-estimation for discrete data: Asymptotic distribution theory and implications
• Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise
• A maximal inequality and dependent strong laws
• Behavior of robust estimators in the regression model with dependent errors
• The behavior of robust estimators on dependent data
• On asymptotically efficient recursive estimation
• Strong convergence of a stochastic approximation algorithm
• On the Strong Mixing Property for Linear Sequences
• Robust Statistics
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