Some Global Optimization Algorithms in Statistics
Kai‐Tai Fang, Fred J. Hickernell, Peter Winker · 1996
. There are many problems in statistics that need some powerful global optimization methods. This paper reviews two efficient methods: SNTO (sequential number-theoretic methods for optimization) and TA (the threshold accepting algorithm). A discussion is given of the applications of these methods to various statistics problems: maximum likelihood estimation, regression analysis, model selection, experimental design, projection pursuit, etc. Key Words and Phrases: Experimental design, global optimization, numbertheoretic methods, nonlinear regression model, projection pursuit, simulated annealing, threshold accepting. Mathematical Subject Classifications 1991: 65K10. 1 Introduction There are many problems in statistics that need powerful algorithms for optimization, for example, maximum likelihood estimation, nonlinear regression, projection pursuit and design of experiments. Let f be a function over a domain G, a subset of R s . We are required to find the global maximum (m...