Introduction to Optimization Methods and their Application in Statistics

Häftad, Engelska, 2011

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Optimization techniques are used to find the values of a set of parameters which maximize or minimize some objective function of interest. 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.

Produktinformation

Utgivningsdatum2011-10-12
Mått152 x 229 x 12 mm
Vikt168 g
FormatHäftad
SpråkEngelska
Antal sidor88
FörlagSpringer
ISBN9789401079174

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1 An introduction to optimization methods.- 1.1 Introduction.- 1.2 The optimization problem.- 1.3 Some simple examples.- 1.4 Minimization procedures.- 1.5 Constrained minimization.- 1.6 Summary.- 2 Direct search methods.- 2.1 Introduction.- 2.2 Univariate search methods.- 2.3 Multiparameter search methods.- 2.4 Summary.- 3 Gradient methods.- 3.1 Introduction.- 3.2 The method of steepest descent.- 3.3 The Newton—Raphson method.- 3.4 The Davidon—Fletcher—Powell method.- 3.5 The Fletcher—Reeves method.- 3.6 Summary.- 4 Some examples of the application of optimization techniques to statistical problems.- 4.1 Introduction.- 4.2 Maximum likelihood estimation.- 4.3 Maximum likelihood estimation for incomplete data.- 4.4 Summary.- 5 Optimization in regression problems.- 5.1 Introduction.- 5.2 Regression.- 5.3 Non-linear regression.- 5.4 Log-linear and linear logistic models.- 5.5 The generalized linear model.- 5.6 Summary.- 6 Optimization in multivariate analysis.- 6.1 Introduction.- 6.2 Maximum likelihood factor analysis.- 6.3 Cluster analysis.- 6.4 Multidimensional scaling.- 6.5 Summary.- Appendix: exercises.- References.