A quasi-Newton method for minimum trace factor analysis
Abbreviated Journal Title
J. Stat. Comput. Simul.
minimum trace factor analysis; constrained minimum trace factor; analysis; weighted minimum trace factor analysis; reliability; Han-Powell algorithm; LOWER BOUNDS; RELIABILITY; Computer Science, Interdisciplinary Applications; Statistics &; Probability
In the past several algorithms have been given to solve the minimum trace factor analysis (MTFA) and the constrained minimum trace factor analysis (CMTFA) problems. Some of these algorithms, depending on the initial value, may converge to points that are not the solution to the above problems, some converge linearly, and some are quadratically convergent but are somewhat difficult to implement. In this paper we propose modified Han-Powell algorithms to solve the MTFA and CMTFA problems. The modifications deal with the problem of multiple eigenvalues. The proposed algorithms are globally convergent and their speed is locally superlinear. We also give a modified Han-Powell algorithm to solve the weighted minimum trace factor analysis (WMTFA) problem. This method is also locally superlinear and is simpler to implement as compared to methods proposed earlier. Four examples are given to show the performance of the proposed algorithms. More generally, our experience with these algorithms shows that, starting at arbitrary paints, they converge to the solution in a small number of iterations and reasonable time.
Journal of Statistical Computation and Simulation
"A quasi-Newton method for minimum trace factor analysis" (1998). Faculty Bibliography 1990s. 2289.