eBook ISBN:  9780821878774 
Product Code:  CONM/287.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821878774 
Product Code:  CONM/287.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 287; 2001; 340 ppMSC: Primary 05; 60; 62; Secondary 13; 15; 20; 30
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 grouptheoretic 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.
ReadershipGraduate students and research mathematicians interested in combinatorics, probability theory, stochastic processes, and statistics.

Table of Contents

Articles

John Aitchison — Simplicial inference [ MR 1873662 ]

JeanFrançois Burnol — A note on Nyman’s equivalent formulation of the Riemann hypothesis [ MR 1873663 ]

Dominique Collombier and Astrid Jourdan — On the construction of linear orthogonal arrays by extension [ MR 1873664 ]

Alessandro Di Bucchianico and Daniel E. Loeb — A coordinatefree approach to multivariate exponential families [ MR 1873665 ]

Morris L. Eaton and William D. Sudderth — Best invariant predictive distributions [ MR 1873666 ]

Werner Ehm — A family of probability densities related to the Riemann zeta function [ MR 1873667 ]

Steven N. Evans — Local field $U$statistics [ MR 1873668 ]

Philip Feinsilver and Jerzy Kocik — Krawtchouk matrices from classical and quantum random walks [ MR 1873669 ]

Yonghong Gao and John I. Marden — Some rankbased hypothesis tests for covariance structure and conditional independence [ MR 1873670 ]

Piotr Graczyk — Gaussian measures as limits on irreducible symmetric spaces and cones [ MR 1873671 ]

Rameshwar D. Gupta and Donald St. P. Richards — The covariance structure of the multivariate Liouville distributions [ MR 1873672 ]

Inge S. Helland — Reduction of regression models under symmetry [ MR 1873673 ]

Peter T. Kim and Donald St. P. Richards — Deconvolution density estimation on compact Lie groups [ MR 1873674 ]

Chris A. J. Klaassen, EunJoo Lee and Frits H. Ruymgaart — On efficiency of indirect estimation of nonparametric regression functions [ MR 1873675 ]

Tõnu Kollo and Dietrich von Rosen — Patterned matrices treated via linear spaces [ MR 1873676 ]

Steven P. Lalley — Random walks on regular languages and algebraic systems of generating functions [ MR 1873677 ]

Gérard Letac and Hélène Massam — The normal quasiWishart distribution [ MR 1873678 ]

Teresa Neeman and Ted Chang — Rank score statistics for spherical data [ MR 1873679 ]

Michael D. Perlman — Graphical model search via essential graphs [ MR 1873680 ]

Giovanni Pistone, Eva Riccomagno and Henry P. Wynn — Computational commutative algebra in discrete statistics [ MR 1873681 ]

Akimichi Takemura and Satoshi Kuriki — Maximum covariance difference test for equality of two covariance matrices [ MR 1873682 ]

Marlos A. G. Viana — The covariance structure of random permutation matrices [ MR 1868878 ]

Ernst Wit and Peter McCullagh — The extendibility of statistical models [ MR 1868879 ]


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

Articles

John Aitchison — Simplicial inference [ MR 1873662 ]

JeanFrançois Burnol — A note on Nyman’s equivalent formulation of the Riemann hypothesis [ MR 1873663 ]

Dominique Collombier and Astrid Jourdan — On the construction of linear orthogonal arrays by extension [ MR 1873664 ]

Alessandro Di Bucchianico and Daniel E. Loeb — A coordinatefree approach to multivariate exponential families [ MR 1873665 ]

Morris L. Eaton and William D. Sudderth — Best invariant predictive distributions [ MR 1873666 ]

Werner Ehm — A family of probability densities related to the Riemann zeta function [ MR 1873667 ]

Steven N. Evans — Local field $U$statistics [ MR 1873668 ]

Philip Feinsilver and Jerzy Kocik — Krawtchouk matrices from classical and quantum random walks [ MR 1873669 ]

Yonghong Gao and John I. Marden — Some rankbased hypothesis tests for covariance structure and conditional independence [ MR 1873670 ]

Piotr Graczyk — Gaussian measures as limits on irreducible symmetric spaces and cones [ MR 1873671 ]

Rameshwar D. Gupta and Donald St. P. Richards — The covariance structure of the multivariate Liouville distributions [ MR 1873672 ]

Inge S. Helland — Reduction of regression models under symmetry [ MR 1873673 ]

Peter T. Kim and Donald St. P. Richards — Deconvolution density estimation on compact Lie groups [ MR 1873674 ]

Chris A. J. Klaassen, EunJoo Lee and Frits H. Ruymgaart — On efficiency of indirect estimation of nonparametric regression functions [ MR 1873675 ]

Tõnu Kollo and Dietrich von Rosen — Patterned matrices treated via linear spaces [ MR 1873676 ]

Steven P. Lalley — Random walks on regular languages and algebraic systems of generating functions [ MR 1873677 ]

Gérard Letac and Hélène Massam — The normal quasiWishart distribution [ MR 1873678 ]

Teresa Neeman and Ted Chang — Rank score statistics for spherical data [ MR 1873679 ]

Michael D. Perlman — Graphical model search via essential graphs [ MR 1873680 ]

Giovanni Pistone, Eva Riccomagno and Henry P. Wynn — Computational commutative algebra in discrete statistics [ MR 1873681 ]

Akimichi Takemura and Satoshi Kuriki — Maximum covariance difference test for equality of two covariance matrices [ MR 1873682 ]

Marlos A. G. Viana — The covariance structure of random permutation matrices [ MR 1868878 ]

Ernst Wit and Peter McCullagh — The extendibility of statistical models [ MR 1868879 ]