Extended iterative weighted least squares: Estimation of a linear model in the presence of complications

In: Naval research logistics: an international journal, Band 18, Heft 2, S. 243-276

Abstract

AbstractThis paper introduces an extended iterative weighted least squares procedure, denoted by EIWLS, for solution of a classical problem in analysis of scientific and technical information: estimation in the presence of complications, of the coefficients for linearly independent component signals in a linear model, from observations on the component signals and a composite signal containing the linear model plus noise which is nonstationary and/or correlated with unknown covariance matrix. An iterative weighted least squares procedure, denoted by IWLS, is developed for estimation in the absence of complications. Then IWLS is extended to perform the estimation subject to: (1) estimators being consistent with a priori information describing the random variation of coefficients over all possible states of nature (e. g., all systems of a specified type from a production process); (2) utilization of data from all pertinent channels in the estimation of coefficients which appear in the linear models for more than one data channel; and (3) replacment of the linear model by a new linear model containing only representative component signals which are highly‐descriptive, but not highly‐related, when there is a large number of component signals in the linear model and some of them are highly‐related. FORTRAN computer programs have been written to implement IWLS and EIWLS on the IBM 7094 for the case of nonstationary and uncorrelated noise.