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

Gamboa, F.; Gassiat, E.

Ann. Stat. 24, No. 5, 1964-1981 (1996).

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.

MSC:

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

Keywords:

deterministic filter; contrast function; T-system; discrete linear systems; blind deconvolution problem; finite discrete support; transfer linear system; AR systems