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Algebraic Methods in Statistics and Probability
Edited by: Marlos A. G. Viana, University of Illinois at Chicago, IL, and Donald St. P. Richards, University of Virginia, Charlottesville, VA
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Contemporary Mathematics
2001; 340 pp; softcover
Volume: 287
ISBN-10: 0-8218-2687-5
ISBN-13: 978-0-8218-2687-4
List Price: US$92
Member Price: US$73.60
Order Code: CONM/287
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Algebraic methods and arguments in statistics and probability are well known, from Gauss's least squares principle through Fisher's method of variance decomposition. The relevance of group-theoretic arguments, for example, became evident in the 1980s. Such techniques continue to be of interest today, along with other developments, such as the use of graph theory in modelling complex stochastic systems.

This volume is based on lectures presented at the AMS Special Session on Algebraic Methods and Statistics held at the University of Notre Dame (Indiana) and on contributed articles solicited for this volume. The articles are intended to foster communication between representatives of the diverse scientific areas in which these functions are utilized and to further the trend of utilizing algebraic methods in the areas of statistics and probability.

This is one of few volumes devoted to the subject of algebraic methods in statistics and probability. The wide range of topics covered in this volume demonstrates the vigorous level of research and opportunities ongoing in these areas.

Readership

Graduate students and research mathematicians interested in combinatorics, probability theory, stochastic processes, and statistics.

Table of Contents

  • J. Aitchison -- Simplicial inference
  • J.-F. Burnol -- A note on Nyman's equivalent formulation of the Riemann hypothesis
  • D. Collombier and A. Jourdan -- On the construction of linear orthogonal arrays by extension
  • A. Di Bucchianico and D. E. Loeb -- A coordinate-free approach to multivariate exponential families
  • M. L. Eaton and W. D. Sudderth -- Best invariant predictive distributions
  • W. Ehm -- A family of probability densities related to the Riemann zeta function
  • S. N. Evans -- Local field \(U\)-statistics
  • P. Feinsilver and J. Kocik -- Krawtchouk matrices from classical and quantum random walks
  • Y. Gao and J. I. Marden -- Some rank-based hypothesis tests for covariance structure and conditional independence
  • P. Graczyk -- Gaussian measures as limits on irreducible symmetric spaces and cones
  • R. D. Gupta and D. St. Richards -- The covariance structure of the multivariate Liouville distributions
  • I. S. Helland -- Reduction of regression models under symmetry
  • P. T. Kim and D. St. Richards -- Deconvolution density estimation on compact Lie groups
  • C. A. J. Klaassen, E.-J. Lee, and F. H. Ruymgaart -- On efficiency of indirect estimation of nonparametric regression functions
  • T. Kollo and D. von Rosen -- Patterned matrices treated via linear spaces
  • S. P. Lalley -- Random walks on regular languages and algebraic systems of generating functions
  • G. Letac and H. Massam -- The normal quasi-Wishart distribution
  • T. Neeman and T. Chang -- Rank score statistics for spherical data
  • M. D. Perlman -- Graphical model search via essential graphs
  • G. Pistone, E. Riccomagno, and H. P. Wynn -- Computational commutative algebra in discrete statistics
  • A. Takemura and S. Kuriki -- Maximum covariance difference test for equality of two covariance matrices
  • M. A. G. Viana -- The covariance structure of random permutation matrices
  • E. Wit and P. McCullagh -- The extendibility of statistical models
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