A NON-ITERATIVE ALGORITHM FOR LEAST SQUARES ESTIMATION OF MISSING VALUES IN ANY ANALYSIS OF VARIANCE DESIGN.
Abstract
An algorithm has been presented for filling in least squares estimates of m missing values. The method is non-iterative and requires only those subroutines already in use by the program designed to handle complete data plus a subroutine to find the inverse of an mxm symmetric matrix. For one missing value, this algorithm is obviously 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 the mxm matrix. For many missing values (say, greater than 10), this non-iterative method will probably 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 third generation computers. In addition, an iterative algorithm does not produce a warning if there is a singular pattern of missing values. The above described non-iterative method should discover the existence of such a pattern when trying to invert R. Work is currently being done to extend the non-iterative approach to insert 'intelligent' least squares missing values in the singular use. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 18, 1970
- Accession Number
- AD0702070
Entities
People
- Donald B. Rubin
Organizations
- Harvard University