Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms

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Abstract
A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.