A method of sieves for regularizing maximum-likelihood spectrum estimates

Summary form only given, as follows. Maximum-likelihood (ML) spectrum estimation is a notorious ill-posed problem. The authors are concerned with the use of a new regularization method for addressing this fundamental issue. They recommend a method of sieves, based on the following concepts. The spectrum belongs to a subset of some Hilbert space of functions over which a complete set of nonorthogonal basis functions is defined. The spectrum is then represented by a countable set of coefficients in a nonorthogonal series expansion. By defining an appropriate sieve on this countable set, the problem reduces to maximum-likelihood estimation of the parameters in the sieve. Three main attractive features of this approach are: (1) the nonorthogonal expansion is a convenient framework for defining the sieve and including a priori information; (2) mean-square consistence of the estimates can be expected; (3) a tractable alternating maximization algorithm for estimating the parameters has been derived. The setup of this problem is very general and can be applied without major difficulties to the estimation of higher dimensional spectral functions.