The Annals of Statistics

Blind deconvolution of discrete linear systems

F. Gamboa and E. Gassiat

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362305

Digital Object Identifier
doi:10.1214/aos/1069362305

Mathematical Reviews number (MathSciNet)
MR1421156

Zentralblatt MATH identifier
0867.62073

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

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

Citation

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


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