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October 1996 Blind deconvolution of discrete linear systems
F. Gamboa, E. Gassiat
Ann. Statist. 24(5): 1964-1981 (October 1996). DOI: 10.1214/aos/1069362305


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.


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F. Gamboa. E. Gassiat. "Blind deconvolution of discrete linear systems." Ann. Statist. 24 (5) 1964 - 1981, October 1996.


Published: October 1996
First available in Project Euclid: 20 November 2003

zbMATH: 0867.62073
MathSciNet: MR1421156
Digital Object Identifier: 10.1214/aos/1069362305

Primary: 62G05 , 62M09 , 62M10

Keywords: $T$-system , contrast function , Deconvolution , discrete linear systems

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 5 • October 1996
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