| Edition |
2nd ed. |
| Description |
1 online resource (xvi, 447 pages) : illustrations. |
|
data file |
| Physical Medium |
polychrome |
| Series |
Cambridge series in statistical and probabilistic mathematics ; [32]
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Cambridge series on statistical and probabilistic mathematics ; 32.
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| Bibliography |
Includes bibliographical references and indexes. |
| Contents |
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. 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. |
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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. |
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6. Eigenproblems -- 6.1. Introduction -- 6.2. Theory -- 6.3. Power Methods -- 6.4. Symmetric Eigenproblem and Tridiagonalization -- 6.5. 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. |
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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. |
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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. |
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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. |
| Summary |
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical statistics -- Data processing.
|
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Mathematical statistics -- Data processing. |
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Numerical analysis.
|
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Numerical analysis. |
| Genre/Form |
Electronic books.
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Electronic book.
|
| Other Form: |
Print version: Monahan, John F. Numerical methods of statistics. 2nd ed. Cambridge ; New York : Cambridge University Press, ©2011 9780521191586 (DLC) 2011287063 (OCoLC)708741707 |
| ISBN |
9781139082112 (electronic book) |
|
1139082116 (electronic book) |
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9781139079846 (e-book) |
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1139079840 (e-book) |
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9781139077552 (electronic book) |
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1139077554 (electronic book) |
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9780511977176 (electronic book) |
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0511977174 (electronic book) |
|
9780521191586 (hardback) |
|
0521191580 (hardback) |
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9780521139519 (paperback) |
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0521139511 (paperback) |
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