Biased estimation for nonparametric identification of linear systems

Abstract A technique for solving convolution-type integral equations, previously investigated by the author for the inverse problem of radiography, is extended in this article to biological identification problems. The properties of solutions to convolution-type integral equations are formulated in terms of the eigenvalues of a circulant matrix, the eigenvalues being obtained by diagonalization by the discrete Fourier transform. Statistical properties of the solution, the bias and covariance matrix, are derived, and a discrete Fourier transform technique for computing the covariance matrix is also derived. A brief criticism of biological identification problems in the published literature is also given.