Annals of Statistics

Blind deconvolution of discrete linear systems

F. Gamboa and E. Gassiat

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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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Ann. Statist., Volume 24, Number 5 (1996), 1964-1981.

First available in Project Euclid: 20 November 2003

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62M09: Non-Markovian processes: estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Deconvolution contrast function $T$-system discrete linear systems


Gamboa, F.; Gassiat, E. Blind deconvolution of discrete linear systems. Ann. Statist. 24 (1996), no. 5, 1964--1981. doi:10.1214/aos/1069362305.

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