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Author Monahan, John F
Title Numerical Methods of Statistics
Imprint New York : Cambridge University Press, 2011
©2011
book jacket
Edition 2nd ed
Descript 1 online resource (465 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Cambridge Series in Statistical and Probabilistic Mathematics
Cambridge Series in Statistical and Probabilistic Mathematics
Note Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface to the Second Edition -- Preface to the First Edition -- 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 Matric -- 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 -- (A) Roy's Test -- (B) Principal Components -- (C) Moore-Penrose Pseudoinverse -- (D) PC Scores and Regression -- (E) Canonical Correlation -- (F) Procrustes Rotation -- 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 -- (A) Normal Distribution -- (B) Logarithm of the Normal Distribution Function -- (C) Student's t Distribution -- (D) Chi-Square, Poisson, and Incomplete Gamma -- (E) F and Beta Distributions -- (F) Inverse Normal -- (G) Bivariate Normal -- 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 -- (A) Simulation Experiments in Statistics -- (B) Hypothesis Tests -- (C) Bayesian Analysis -- 10.3 One-Dimensional Quadrature -- 10.4 Numerical Integration in Two or More Variables -- (A) Integration over a Triangle -- (B) Integration on Surface of a Sphere -- (C) The Curse and Monte Carlo Integration -- 10.5 Uniform Pseudorandom Variables -- (A) Testing Random Number Generators -- (B) Linear Congruential Generators -- (C) Shift Register Methods -- (D) Recommendations -- (E) Multiple Generators -- 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 -- (A) Transformations -- (B) Acceptance/Rejection -- (C) Ratio of Uniforms -- 11.3 Algorithms for Continuous Distributions -- (A) Normal Distribution -- (B) Exponential Distribution -- (C) Student's t and Cauchy -- (D) Gamma, Chi-Square, and Chi -- (E) Logistic and Laplace -- (F) Beta, F, and Dirichlet -- (G) Noncentral Chi-Square, F, and t -- (H) Pareto and Weibull -- (I) Multivariate Normal and t -- Wishart -- 11.4 General Methods for Discrete Distributions -- (A) Discrete Inversion -- (B) Acceptance/Rejection -- (C) Ratio of Uniforms -- (D) Walker's Alias Method -- 11.5 Algorithms for Discrete Distributions -- (A) Geometric and Negative Binomial -- (B) Binomial -- (C) Poisson -- (D) Hypergeometric -- 11.6 Other Randomizations
(A) Random Permutations -- (B) Random Sampling -- (C) Random Contingency Tables -- 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 -- (A) Pearson's Chi-Square -- (B) Kolmogorov-Smirnov -- (C) Anderson-Darling -- (D) Quasirandom Sequences -- 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 -- (A) Plot the Data -- (B) Gelman and Rubin -- (C) Geweke -- (D) Heidelberger and Welch -- (E) Raftery and Lewis -- (F) Dickey-Fuller -- 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 -- (A) Time Series -- (B) Characteristic Functions of Discrete Random Variables -- (C) Convolutions of Continuous Random Variables by Discretization -- (D) Inverting the Characteristic Function of Continuous Random Variables -- (E) Weighted Sums of Chi-Square Random Variables -- 14.8 Combinatorial Problems -- (A) Counting in Base B -- (B) Subsets of Size K from N -- (C) All Permutations -- Programs and Demonstrations -- Exercises -- References -- Author Index -- Subject Index
This second edition explains how computer software is designed to perform the tasks required for sophisticated statistical analysis
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Monahan, John F. Numerical Methods of Statistics New York : Cambridge University Press,c2011 9780521191586
Subject Mathematical statistics -- Data processing.;Numerical analysis
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