Introduction to Optimization Methods and their Application in Statistics

Optimization techniques are used to find the values of a set of parameters which maximize or minimize some objective function of interest. Such methods have become of great importance in statistics for estimation, model fitting, etc. This text attempts to give a brief introduction to optimization methods and their use in several important areas of statistics. It does not pretend to provide either a complete treatment of optimization techniques or a comprehensive review of their application in statistics; such a review would, of course, require a volume several orders of magnitude larger than this since almost every issue of every statistics journal contains one or other paper which involves the application of an optimization method. It is hoped that the text will be useful to students on applied statistics courses and to researchers needing to use optimization techniques in a statistical context. Lastly, my thanks are due to Bertha Lakey for typing the manuscript. Front Matter....Pages i-vii An introduction to optimization methods....Pages 1-10 Direct search methods....Pages 11-20 Gradient methods....Pages 21-27 Some examples of the application of optimization techniques to statistical problems....Pages 28-41 Optimization in regression problems....Pages 42-58 Optimization in multivariate analysis....Pages 59-79 Back Matter....Pages 80-88