An Inequality for Rational Functions with Applications to Some Statistical Estimation Problems

The well-known Baum-Eagon ineauality 131 provides an effective iterative scheme for finding a local maximum for homogeneous polynomials with positive coefficients over a domain of probability values. However, in many applications we are interested in maximizing a general rational function. We extend the Baum-Eagon inequality to rational functions. We briefly describe some of the applications of this inequality to statistical estimation problems. © 1991 IEEE