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Author:

Monahan, John F.

Title:

Numerical methods of statistics / John F. Monahan.

Edition:

2nd ed.

Publisher:

Cambridge University Press,

Copyright Date:

c2011

Description:

xvi, 447 p. : ill. ; 26 cm.

Subject:

Mathematical statistics--Data processing.
Numerical analysis.

Notes:

Includes bibliographical references and index.

Contents:

3.8. 1. References 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
5.14. References 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
8.4. First Digression: Stopping and Condition 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
10.3. One-Dimensional Quadrature 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
12.6. Laplace Approximations 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
14.8. References. 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.

Series:

Cambridge series in statistical and probabilistic mathematics ; [32]

ISBN:

9780521139519 (pbk.)
0521139511 (pbk.)
0521191580
9780521191586

OCLC:

(OCoLC)708741707

LCCN:

2011287063

Locations:

USUX851 -- Iowa State University - Parks Library (Ames)