Speed of convergence for the blind deconvolution of a linear system with discrete random input
成果类型：
Article
署名作者：
Gassiat, E; Gautherat, E
署名单位：
Universite Paris Saclay; Universite de Reims Champagne-Ardenne
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1999
页码：
1684-1705
关键词：
摘要：
In a recent paper, we proposed a new estimation method for the blind deconvolution of a linear system with discrete random input, when the observations may be noise perturbed. We give here asymptotic properties of the estimators in the parametric situation. With nonnoisy observations, the speed of convergence is governed by the Ii-tail of the inverse filter. which may have an exponential decrease. With noisy observations, the estimator satisfies a limit theorem with known distribution, which allows for the construction of confidence regions. To our knowledge, this is the first precise asymptotic result in the noisy blind deconvolution problem with an unknown level of noise. We also extend results concerning Hankel's estimation to Toeplitz's estimation and prove a formula to compute Toeplitz forms that may have interest in itself.