On the statistical analysis of quantized Gaussian AR(1) processes

A discrete‐time stable Gaussian autoregressive process is considered, which is observed with a fixed precision only. A law of large numbers—uniformly in the autoregression, mean and variance parameters—is proved for the log‐likelihood function of the observations through establishing a mixing proper...

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Bibliographic Details
Published in:International journal of adaptive control and signal processing 2010-06, Vol.24 (6), p.490-507
Main Author: Rasonyi, M
Format: Article
Language:English
Subjects:
Adaptive control
Autoregressive processes
Gaussian
Gaussian ARMA processes
Law
law of large numbers
log-likelihood function
maximum likelihood estimators
quantized observations
Signal processing
Stability
Statistical analysis
system identification
Variance
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Summary:A discrete‐time stable Gaussian autoregressive process is considered, which is observed with a fixed precision only. A law of large numbers—uniformly in the autoregression, mean and variance parameters—is proved for the log‐likelihood function of the observations through establishing a mixing property. Exponential stability of the corresponding filter is also derived. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:0890-6327
1099-1115
DOI:10.1002/acs.1145