Numerical methods of statistics [electronic resource] / John F. Monahan
- Author
- Monahan, John F.
- Published
- Cambridge : Cambridge University Press, 2011.
- Edition
- 2nd ed.
- Physical Description
- xvi, 447 pages : illustrations
- Additional Creators
- ebrary, Inc
Access Online
- Series
- Contents
- Machine generated contents note: 1.Algorithms and Computers -- 1.1.Introduction -- 1.2.Computers -- 1.3.Software and Computer Languages -- 1.4.Data Structures -- 1.5.Programming Practice -- 1.6.Some Comments on R -- References -- 2.Computer Arithmetic -- 2.1.Introduction -- 2.2.Positional Number Systems -- 2.3.Fixed Point Arithmetic -- 2.4.Floating Point Representations -- 2.5.Living with Floating Point Inaccuracies -- 2.6.The Pale and Beyond -- 2.7.Conditioned Problems and Stable Algorithms -- Programs and Demonstrations -- Exercises -- References -- 3.Matrices and Linear Equations -- 3.1.Introduction -- 3.2.Matrix Operations -- 3.3.Solving Triangular Systems -- 3.4.Gaussian Elimination -- 3.5.Cholesky Decomposition -- 3.6.Matrix Norms -- 3.7.Accuracy and Conditioning -- 3.8.Matrix Computations in R -- Programs and Demonstrations -- Exercises -- References -- 4.More Methods for Solving Linear Equations -- 4.1.Introduction -- 4.2.Full Elimination with Complete Pivoting -- 4.3.Banded Matrices -- 4.4.Applications to Arma Time-Series Models -- 4.5.Toeplitz Systems -- 4.6.Sparse Matrices -- 4.7.Iterative Methods -- 4.8.Linear Programming -- Programs and Demonstrations -- Exercises -- References -- 5.Regression Computations -- 5.1.Introduction -- 5.2.Condition of the Regression Problem -- 5.3.Solving the Normal Equations -- 5.4.Gram-Schmidt Orthogonalization -- 5.5.Householder Transformations -- 5.6.Householder Transformations for Least Squares -- 5.7.Givens Transformations -- 5.8.Givens Transformations for Least Squares -- 5.9.Regression Diagnostics -- 5.10.Hypothesis Tests -- 5.11.Conjugate Gradient Methods -- 5.12.Doolittle, the Sweep, and All Possible Regressions -- 5.13.Alternatives to Least Squares -- 5.14.Comments -- Programs and Demonstrations -- Exercises -- References -- 6.Eigenproblems -- 6.1.Introduction -- 6.2.Theory -- 6.3.Power Methods -- 6.4.The Symmetric Eigenproblem and Tridiagonalization -- 6.5.The Qr Algorithm -- 6.6.Singular Value Decomposition -- 6.7.Applications -- 6.8.Complex Singular Value Decomposition -- Programs and Demonstrations -- Exercises -- References -- 7.Functions: Interpolation, Smoothing, and Approximation -- 7.1.Introduction -- 7.2.Interpolation -- 7.3.Interpolating Splines -- 7.4.Curve Fitting with Splines: Smoothing and Regression -- 7.5.Mathematical Approximation -- 7.6.Practical Approximation Techniques -- 7.7.Computing Probability Functions -- Programs and Demonstrations -- Exercises -- References -- 8.Introduction to Optimization and Nonlinear Equations -- 8.1.Introduction -- 8.2.Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- 8.3.Root Finding -- 8.4.First Digression: Stopping and Condition -- 8.5.Multivariate Newton's Methods -- 8.6.Second Digression: Numerical Differentiation -- 8.7.Minimization and Nonlinear Equations -- 8.8.Condition and Scaling -- 8.9.Implementation -- 8.10.A Non-Newton Method: Nelder-Mead -- Programs and Demonstrations -- Exercises -- References -- 9.Maximum Likelihood and Nonlinear Regression -- 9.1.Introduction -- 9.2.Notation and Asymptotic Theory of Maximum Likelihood -- 9.3.Information, Scoring, and Variance Estimates -- 9.4.An Extended Example -- 9.5.Concentration, Iteration, and the Em Algorithm -- 9.6.Multiple Regression in the Context of Maximum Likelihood -- 9.7.Generalized Linear Models -- 9.8.Nonlinear Regression -- 9.9.Parameterizations and Constraints -- Programs and Demonstrations -- Exercises -- References -- 10.Numerical Integration and Monte Carlo Methods -- 10.1.Introduction -- 10.2.Motivating Problems -- 10.3.One-Dimensional Quadrature -- 10.4.Numerical Integration in Two or More Variables -- 10.5.Uniform Pseudorandom Variables -- 10.6.Quasi-Monte Carlo Integration -- 10.7.Strategy and Tactics -- Programs and Demonstrations -- Exercises -- References -- 11.Generating Random Variables from Other Distributions -- 11.1.Introduction -- 11.2.General Methods for Continuous Distributions -- 11.3.Algorithms for Continuous Distributions -- 11.4.General Methods for Discrete Distributions -- 11.5.Algorithms for Discrete Distributions -- 11.6.Other Randomizations -- 11.7.Accuracy in Random Number Generation -- Programs and Demonstrations -- Exercises -- References -- 12.Statistical Methods for Integration and Monte Carlo -- 12.1.Introduction -- 12.2.Distribution and Density Estimation -- 12.3.Distributional Tests -- 12.4.Importance Sampling and Weighted Observations -- 12.5.Testing Importance Sampling Weights -- 12.6.Laplace Approximations -- 12.7.Randomized Quadrature -- 12.8.Spherical-Radial Methods -- Programs and Demonstrations -- Exercises -- References -- 13.Markov Chain Monte Carlo Methods -- 13.1.Introduction -- 13.2.Markov Chains -- 13.3.Gibbs Sampling -- 13.4.Metropolis-Hastings Algorithm -- 13.5.Time-Series Analysis -- 13.6.Adaptive Acceptance/Rejection -- 13.7.Diagnostics -- Programs and Demonstrations -- Exercises -- References -- 14.Sorting and Fast Algorithms -- 14.1.Introduction -- 14.2.Divide and Conquer -- 14.3.Sorting Algorithms -- 14.4.Fast Order Statistics and Related Problems -- 14.5.Fast Fourier Transform -- 14.6.Convolutions and the Chirp-z Transform -- 14.7.Statistical Applications of the Fft -- 14.8.Combinatorial Problems -- Programs and Demonstrations -- Exercises -- References.
- Subject(s)
- ISBN
- 9780511977176 (electronic bk.)
9780521191586 (hbk.)
9780521139519 (pbk.) - Bibliography Note
- Includes bibliographical references and indexes.
- Reproduction Note
- Electronic reproduction. Palo Alto, Calif. : ebrary, 2011. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.
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