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Empirical Processes with Applications to Statistics

Empirical Processes with Applications to Statistics

Part of Classics in Applied Mathematics

  • Date Published: September 2009
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716849

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  • Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition.

    • A classic originally published in 1986
    • A valuable resource for researchers in statistical theory, probability theory, biostatistics, econometrics and computer science
    • Contains a solid treatment of Martingale approaches to right-censored data
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    Product details

    • Date Published: September 2009
    • format: Paperback
    • isbn: 9780898716849
    • length: 948 pages
    • dimensions: 230 x 150 x 48 mm
    • weight: 1.34kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface for Classics Edition
    Preface
    1. Introduction and survey of results
    2. Foundations, special spaces and special processes
    3. Convergence and distributions of empirical processes
    4. Alternatives and processes of residuals
    5. Integral test of fit and estimated empirical process
    6. Martingale methods
    7. Censored data: the product-limit estimator
    8. Poisson and exponential representations
    9. Some exact distributions
    10. Linear and nearly linear bounds on the empirical distribution function Gn
    11. Exponential inequalities and ║∙/q║ -metric convergence of Un and Vn
    12. The Hungarian constructions of Kn, Un, and Vn
    13. Laws of the iterated logarithm associated with Un and Vn
    14. Oscillations of the empirical process
    15. The uniform empirical difference process Dn≡Un + Vn
    16. The normalized uniform empirical process Zn and the normalized uniform quantile process
    17. The uniform empirical process indexed by intervals and functions
    18. The standardized quantile process Qn
    19. L-statistics
    20. Rank statistics
    21. Spacing
    22. Symmetry
    23. Further applications
    24. Large deviations
    25. Independent but not identically distributed random variable
    26. Empirical measures and processes for general spaces
    Appendix A. Inequalities and miscellaneous
    Appendix B. Counting processes Martingales
    References
    Errata
    Author index
    Subject index.

  • Authors

    Galen R. Shorack, University of Washington
    Galen R. Shorack is a Professor of Statistics at the University of Washington. He is a Fellow of the Institute of Mathematical Statistics and has written a graduate level text on probability theory.

    Jon A. Wellner, University of Washington
    Jon A. Wellner is a Professor of Statistics at the University of Washington. He is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the American Association for the Advancement of Science. He has written three other books on probability and statistics.

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