Statistical Computing

Martorell, Sebastián; Guedes Soares, Carlos; Barnett, Julie

Introduction, Orientation Purpose, Prerequisites Presentation of Algorithms Computer Organization, Introduction, Components of the Digital Computer System, Representation of Numeric Values Floating and Fixed-Point Arithmetic Operations, Error in Floating-Point Computation, Introduction, Types of Error Error Due to Approximation, Imposed by the Compute Analyzing Error in a Finite Process, Rounding Error in Floating-Point Operations, Rounding Error in Two Common Floating-Point Calculations, Condition and Numerical Stability, Other Methods of Assessing Error in Computations, Summary Programming and Statistical Software, Programming Languages: Introduction, Components of Programming Languages, Program Development Statistical Software ,Approximating Probabilities and Percentage Points in Selected Probability Distributions, Notation and General Considerations, General Methods in Approximation, The Normal Distribution, Student's t Distribution, The Beta Distribution, F Distribution, Chi-Square Distribution, Random Numbers: Generation, Tests, and Applications, Introduction, Generation of Uniform Random Numbers, Tests of Random Number Generators, General Techniques for Generation of Nonuniform Random Variates, Generation of Variates from Specific Distributions, Applications Selected Computational Methods in Linear Algebra, Introduction, Methods Based on Orthogonal Transformations, Gaussian Elimination and the Sweep Operator, Cholesky Decomposition and Rank-One Update, Summary, Computational Methods for Multiple Linear Regression, Analysis, Basic Computational Methods, Regression, Model Building Multiple Regression Under Linear Restrictions, Computational Methods for Classification Models, Introduction, The Special Case of Balance and Completeness for Fixed-Effects Models, The General Problem for Fixed-Effects Models, Computing Expected Mean Squares and Estimates of Variance Components, Unconstrained Optimization and Nonlinear Regression Preliminaries Methods for Unconstrained Minimization Nonlinear Regression, Computational Methods Test Problems, Model Fitting Based on Criteria, Other Than Least Squares, Introduction, Minimum Lp Norm Estimators, Other Robust Estimators, Biased Estimation Robust Nonlinear Regression Exercises, Selected Multivariate Methods, Introduction Canonical Correlations, Principal Components, Factor Analysis, Multivariate, Analysis of Variance.