Blind deconvolution of discrete linear systems. (English) Zbl 0867.62073

Summary: We study the blind deconvolution problem in the case where the input noise has a finite discrete support and the transfer linear system is not necessarily minimum phase. We propose a new family of estimators built using algebraic considerations. The estimates are consistent under very wide assumptions: The input signal need not be independently distributed; the cardinality of the finite support may be estimated simultaneously. We consider in particular AR systems: In this case, we prove that the estimator of the parameters is perfect a.s. with a finite number of observations.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E10 Estimation and detection in stochastic control theory
62G05 Nonparametric estimation
62M09 Non-Markovian processes: estimation
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