Numerical methods of statistics

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 mat...

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Detalles Bibliográficos
Autor principal:	Monahan, John F. (-)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Cambridge ; New York : Cambridge University Press 2011.
Edición:	2nd ed
Colección:	EBSCO Academic eBook Collection Complete. Cambridge series in statistical and probabilistic mathematics ; [32]
Acceso en línea:	Conectar con la versión electrónica
Ver en Universidad de Navarra:	https://innopac.unav.es/record=b38422700*spi

Tabla de Contenidos:

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.

Numerical methods of statistics

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