OPTIMALITY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN FIRST-ORDER AUTOREGRESSIVE PROCESSES

DOI10.1111/j.1467-9892.1991.tb00080.xzbMath0733.62094OpenAlexW2128377083MaRDI QIDQ3359620

Michael J. Monsour, Piotr W. Mikulski

Publication date: 1991

Published in: Journal of Time Series Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9892.1991.tb00080.x

zbMATH Keywords

momentsuniform convergenceefficiencyderivativeuniform integrabilityCramér-Rao inequalitymaximum likelihood estimatorbiasasymptotic optimalityAR(1) processfirst-order autoregressive processexistence of unbiased estimatorsminimizing expected mean square errorweighted mean square

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10)

Related Items (7)

Truncated estimation of ratio statistics with application to heavy tail distributions ⋮ Moments of the Limiting Distribution for the Boundary Case in the First Order Autoregressive Process ⋮ A truncated estimation method with guaranteed accuracy ⋮ Non-asymptotic confidence estimation of the parameters in stochastic regression models with Gaussian noises ⋮ On one property of martingales with conditionally Gaussian increments and its application in the theory of nonasymptotic inference ⋮ Guaranteed Estimation of Logarithmic Density Derivative by Dependent Observations ⋮ Sequential fixed accuracy estimation for nonstationary autoregressive processes

Cites Work

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• Asymptotic optimal inference for non-ergodic models
• On attainable Cramèr-Rao type lower bounds for weighted loss functions
• Distribution function inequalities for martingales
• Properties of Predictors for Autoregressive Time Series
• Moments of the Limiting Distribution for the Boundary Case in the First Order Autoregressive Process
• Asymptotic Properties of the Maximum Likelihood Estimate of an Unknown Parameter of a Discrete Stochastic Process
• On the Statistical Treatment of Linear Stochastic Difference Equations

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