A Non‐Iterative Algorithm for Least Squares Estimation of Missing Values in Any Analysis of Variance Design

Donald B. Rubin

Journal of the Royal Statistical Society Series C, 1972, vol. 21, issue 2, 136-141

Abstract: An algorithm is presented for filling in least squares estimates of m missing values in any analysis of variance design. The method is non‐iterative and requires only those subroutines already in use by a program designed to handle complete data plus a subroutine to find the inverse of an m x m symmetric matrix. For one missing value, this algorithm is faster than an iterative one since only two residualizations are needed in order to obtain the exact solution. For m missing values, m +1 residualizations are needed plus the inversion of an m x m matrix R. For many missing values (say, greater than six), this non‐iterative method might be slower than an iterative one. However, for any reasonable number of missing values, the extra time involved would probably not be great, especially on current computers. In addition, an iterative algorithm does not produce a warning if there is a singular pattern of missing values whereas the above described non‐iterative method will discover the existence of such a pattern when trying to invert R.

Date: 1972
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