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On the statistical analysis of quantized Gaussian AR(1) processes
Author(s) -
Rásonyi M.
Publication year - 2010
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1145
Subject(s) - autoregressive model , gaussian , mixing (physics) , mathematics , exponential function , property (philosophy) , gaussian process , star model , exponential family , gaussian filter , stability (learning theory) , variance (accounting) , statistics , statistical physics , computer science , time series , mathematical analysis , physics , autoregressive integrated moving average , economics , philosophy , accounting , epistemology , quantum mechanics , machine learning
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.