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Numerical Analysis for Statisticians

  • Textbook
  • © 2010

Overview

Authors:
  1. Kenneth Lange

    1. David Geffen School of Medicine, Dept. Biomathematics, University of California, Los Angeles, Los Angeles, USA

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  • Serves as a graduate text for a survey of computational statistics
  • Second edition adds material on optimization, MM algorithm, penalty and barrier methods, and model selection via the lasso
  • Other major topics are updated

Part of the book series: Statistics and Computing (SCO)

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Table of contents (27 chapters)

  1. Front Matter

    Pages I-XX
    Download chapter PDF

  2. Recurrence Relations

    • Kenneth Lange
    Pages 1-11

  3. Power Series Expansions

    • Kenneth Lange
    Pages 13-25

  4. Continued Fraction Expansions

    • Kenneth Lange
    Pages 27-38

  5. Asymptotic Expansions

    • Kenneth Lange
    Pages 39-54

  6. Solution of Nonlinear Equations

    • Kenneth Lange
    Pages 55-75

  7. Vector and Matrix Norms

    • Kenneth Lange
    Pages 77-91

  8. Linear Regression and Matrix Inversion

    • Kenneth Lange
    Pages 93-111

  9. Eigenvalues and Eigenvectors

    • Kenneth Lange
    Pages 113-128

  10. Singular Value Decomposition

    • Kenneth Lange
    Pages 129-142

  11. Splines

    • Kenneth Lange
    Pages 143-155

  12. Optimization Theory

    • Kenneth Lange
    Pages 157-188

  13. The MM Algorithm

    • Kenneth Lange
    Pages 189-221

  14. The EM Algorithm

    • Kenneth Lange
    Pages 223-247

  15. Newton’s Method and Scoring

    • Kenneth Lange
    Pages 249-276

  16. Local and Global Convergence

    • Kenneth Lange
    Pages 277-296

  17. Advanced Optimization Topics

    • Kenneth Lange
    Pages 297-332

  18. Concrete Hilbert Spaces

    • Kenneth Lange
    Pages 333-361

  19. Quadrature Methods

    • Kenneth Lange
    Pages 363-377

  20. The Fourier Transform

    • Kenneth Lange
    Pages 379-393
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Keywords

About this book

Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians. In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbs sampling. Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference.

Reviews

From the reviews:

"This book provides reasonably good coverage of numerical methods that are important in statistical applications. ...but overall the text serves as a good introduction to computational statistics." - MATHEMATICAL REVIEWS

From the reviews of the second edition:

“The theory and equations are well defined and easy enough to read. … This book gives you all the details you need for choosing formulas and libraries when implementing Fourier Transforms. … this is a good book … .” (Cats and Dogs with Data, maryannedata.wordpress.com, July, 2013)

“The aim and scope of this edition is to provide upper level undergraduate students, graduate students and even researchers the understanding and working knowledge of different numerical methods. … The book is organized sequentially and is well structured. … The book can be served as a textbook and equally as a reference book. … the book will appeal to a broad interdisciplinary research community. It can also successfully be used as a reference book for practitioners, providing concrete examples, data and exercises of statistical applications.” (Technometrics, Vol. 53 (2), May, 2011)

“This is a comprehensive handbook for anyone with an interest in computational statistics, such as instructors, statisticians, modelers, data mining analysts, and software designers. For a reader with good working knowledge of numerical analysis, the book is useful for understanding the advantages and disadvantages of different numerical methods. … also suitable for students interested in refining their knowledge: a list of problems with gradually increasing difficulty is available, in addition to a list of very carefully chosen references (a real support for the reader).” (Dragos Calitoiu, Mathematical Reviews, Issue 2011 g)

“Numerical Analysis for Statisticians is a wonderful book. It provides most of the necessary background in calculusand enough algebra to conduct rigorous numerical analyses of statistical problems. … I simply enjoyed Numerical Analysis for Statisticians from beginning until end. … Numerical Analysis for Statisticians also is recommended for more senior researchers, and not only for building one or two courses on the bases of statistical computing. … an essential book to hand to graduate students as soon as they enter a statistics program.” (Christian Robert, Chance, Vol. 24 (4), 2011) 

Authors and Affiliations

  • David Geffen School of Medicine, Dept. Biomathematics, University of California, Los Angeles, Los Angeles, USA

    Kenneth Lange

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