Gentle J.E. Optimization Methods for Applications in Statistics

Springer, 2004. – 254 p. – ISBN: 0387403167, 9780387403168Optimization of functions, that is, minimization or maximization, is ubiquitous in statistical methods. Many methods of inference are built on the principle of maximum likelihood, in which an assumed probability density function or a probability function is optimized with respect to its parameters, given the observed realizations of the random variable whose distribution is described by the function. Other methods of inference involve fitting of a model to observed data in such a way that the deviations of the observations from the model are a minimum. Many important methods of statistics are used before any inferences are made. In fact, ideally, statistical methods are considered before data are collected, and the sampling method or the design of the experiment is determined so as to maximize the value of the data for making inferences, usually by minimizing the variance of estimators.Statistical Methods as Optimization Problems
Numerical Computations
Basic Definitions and Properties of Functions
Finding Roots of Equations
Unconstrained Descent Methods in Dense Domains
Unconstrained Combinatorial Optimization; Other Direct Search Methods
Optimization under Constraints
Multiple Extrema and Multiple Objectives
Software for Optimization
Applications in Statistics
Solutions and Hints for Selected Exercises
Notation and DefinitionsAuthor Index
Subject Index