An inequality for rational functions with applications to some statistical estimation problems

• Published in: IEEE transactions on information theory Vol. 37; no. 1; pp. 107 - 113
• Main Authors: Gopalakrishnan, P.S., Kanevsky, D., Nadas, A., Nahamoo, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-01-1991; Institute of Electrical and Electronics Engineers
• Subjects: Algorithm design and analysis; Exact sciences and technology; Hidden Markov models; Iterative algorithms; Markov processes; Mathematical foundations; Mathematics; Maximum likelihood estimation; Mutual information; Polynomials; Probability; Probability and statistics; Sciences and techniques of general use; Signal processing algorithms; Speech recognition; Statistics; Function maximization; Parameter estimation; Fast algorithm; Rational function; Speech recognition; Inequality
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.61108

The well-known Baum-Eagon inequality (1967) 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 the goal is to maximize a general rational function. In view of this, the Baum-Eagon inequality is extended to rational functions. Some of the applications of this inequality to statistical estimation problems are briefly described.< >