Blind source separation-semiparametric statistical approach

The semiparametric statistical model is used to formulate the problem of blind source separation. The method of estimating functions is applied to this problem. It is shown that an estimator of the mixing matrix or its learning version can be described in terms of an estimating function. The statistical efficiencies of these algorithms are studied. The main results are as follows. (1) The space consisting of all the estimating functions is derived. (2) The space is decomposed into the orthogonal sum of the admissible part and a redundant ancillary part. For any estimating function, one can find a better or equally good estimator in the admissible part. (3) The Fisher efficient (that is, asymptotically best) estimating functions are derived. (4) The stability of learning algorithms is studied