Random Matrices

Madan Mehta - Collection Pure and applied mathematics

700 pages, parution le 06/10/2004 (3^eme édition)

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Résumé

This volume focuses on econometric models that confront estimation and inference issues occurring when sample data exhibit spatial or spatiotemporal dependence. This can arise when decisions or transactions of economic agents are related to the behaviour of nearby agents. Dependence of one observation on neighbouring observations violates the typical assumption of independence made in regression analysis. Contributions to this volume by leading experts in the field of spatial econometrics provide details regarding estimation and inference based on a variety of econometric methods including, maximum likelihood, Bayesian and hierarchical Bayes, instrumental variables, generalized method of moments, maximum entropy, non-parametric and spatiotemporal. An overview of spatial econometric models and methods is provided that places contributions to this volume in the context of existing literature. New methods for estimation and inference are introduced in this volume and Monte Carlo comparisons of existing methods are described. In addition to topics involving estimation and inference, approaches to model comparison and selection are set forth along with new tests for spatial dependence and functional form. These methods are applied to a variety of economic problems including: hedonic real estate pricing, agricultural harvests and disaster payments, voting behaviour, identification of edge cities, and regional labour markets. The volume is supported by a web site containing data sets and software to implement many of the methods described by contributors to this volume.

L'auteur - Madan Mehta

Madan Mehta , C.E.A. de Saclay, Gif-sur-Yvette Cedex, France

Sommaire

Introduction
Gaussian ensembles : the joint probability density function for the matrix elements
Gaussian ensembles : the joint probability density function for the eigenvalues
Gaussian ensembles level density
Orthogonal, skew-orthogonal and bi-orthogonal polynomials
Gaussian unitary ensemble
Gaussian orthogonal ensemble
Gaussian symplectic ensemble
Gaussian ensembles : Brownian motion model
Circular ensembles
Circular ensembles (continued)
Circular ensembles : thermodynamics
Gaussian ensemble of anti-symmetric Hermitian matrices
A Gaussian ensemble of Hermitian matrices with unequal real and imaginary parts
Matrices with Gaussian element densities but with no unitary or Hermitian conditions imposed
Statistical analysis of a level-sequence
Selberg's integral and its consequences
Asymptotic behaviour of E[beta](0,s) by inverse scattering
Matrix ensembles and classical orthogonal polynomials
Level spacing functions E[beta](r,s); inter-relations and power series expansions
Fredholm determinants and Painleve equations
Moments of the characteristic polynomial in the three ensembles of random matrices
Hermitian matrices coupled in a chain
Gaussian ensembles : edge of the spectrum
Random permutations, circular unitary ensemble (CUE) and Gaussian unitary ensemble (GUE)
Probability densities of the determinants : Gaussian ensembles
Restricted trace ensembles

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Elsevier
Auteur(s)	Madan Mehta
Collection	Pure and applied mathematics
Parution	06/10/2004
Édition	3^eme édition
Nb. de pages	700
Format	15,5 x 23,5
Couverture	Relié
Poids	1230g
Intérieur	Noir et Blanc
EAN13	9780120884094
ISBN13	978-0-12-088409-4