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Generalized Method of Moments (GMM) has become one of the main statistical tools for the analysis of economic and financial data. This book provides an introduction to the method combined with a unified treatment of GMM statistical theory and a survey of the important developments in the field.

Econometric models. --- Estimation theory. --- Moments method (Statistics). --- Time-series analysis. --- Moments method (Statistics) --- Method of moments (Statistics) --- Mathematical statistics --- Quantitative methods (economics) --- Econometric models --- Time-series analysis --- Estimation theory --- E-books --- Estimating techniques --- Least squares --- Stochastic processes --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Probabilities --- Econometrics --- Mathematical models --- Distribution (Probability theory)

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Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriat

Moments method (Statistics) --- Polynomials. --- Algebra --- Method of moments (Statistics) --- Mathematical statistics --- Distribution (Probability theory) --- Geometry, Algebraic --- Mathematical optimization --- Moment problems (Mathematics) --- Polynomials --- Calculus, Operational --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algebraic geometry --- Geometry

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Moments method (Statistics) --- Moments, Méthodes de (Statistiques) --- -Moments method (Statistics) --- Method of moments (Statistics) --- Moments, Méthodes de (Statistiques) --- Electromagnetism --- Integral equations --- Moments method (Statistics). --- Mathematical models. --- Numerical solutions. --- #TELE:TMIC --- Mathematical statistics --- Distribution (Probability theory) --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Numerical analysis --- Mathematical models --- Numerical solutions --- Electromagnétisme --- Equations intégrales --- Modèles mathématiques --- Solutions numériques --- Electromagnetism - Mathematical models. --- Integral equations - Numerical solutions.

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Quantum mechanics. Quantumfield theory --- Electromagnetism. Ferromagnetism --- Information systems --- Electromagnetism --- Maxwell equations --- Moments method (Statistics) --- Integro-differential equations --- Numerical solutions --- Data processing --- EMC --- elektromagnetisme --- 519.63 --- 681.3*G18 --- 537.8 --- -Maxwell equations --- -Moments method (Statistics) --- Method of moments (Statistics) --- Mathematical statistics --- Distribution (Probability theory) --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- Integrodifferential equations --- Differential equations --- Integral equations --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Numerical methods for solution of partial differential equations --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- 537.8 Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical analysis --- 681.3 *G18 --- Moments, Méthodes des (statistique) --- Maxwell, Équations de --- Électromagnétisme. --- Data processing. --- Solutions numériques --- Traitement des données. --- Maxwell equations - Numerical solutions --- Maxwell equations - Data processing --- Integro-differential equations - Numerical solutions

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The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

Group theory --- Algebraic geometry --- Number theory --- 511.33 --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Gaussian sums --- Homology theory --- Kloosterman sums --- Monodromy groups --- Kloostermann sums --- Sums, Kloosterman --- Sums, Kloostermann --- Exponential sums --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Gauss sums --- Sums, Gaussian --- Analytical and multiplicative number theory. Asymptotics. Sieves etc --- Gaussian sums. --- Kloosterman sums. --- Homology theory. --- Monodromy groups. --- Number theory. --- Nombres, Théorie des. --- Exponential sums. --- Sommes exponentielles. --- Arithmetic --- Arithmétique --- Geometry, Algebraic. --- Géométrie algébrique --- Abelian category. --- Absolute Galois group. --- Absolute value. --- Additive group. --- Adjoint representation. --- Affine variety. --- Algebraic group. --- Automorphic form. --- Automorphism. --- Big O notation. --- Cartan subalgebra. --- Characteristic polynomial. --- Classification theorem. --- Coefficient. --- Cohomology. --- Cokernel. --- Combination. --- Commutator. --- Compactification (mathematics). --- Complex Lie group. --- Complex number. --- Conjugacy class. --- Continuous function. --- Convolution theorem. --- Convolution. --- Determinant. --- Diagonal matrix. --- Dimension (vector space). --- Direct sum. --- Dual basis. --- Eigenvalues and eigenvectors. --- Empty set. --- Endomorphism. --- Equidistribution theorem. --- Estimation. --- Exactness. --- Existential quantification. --- Exponential sum. --- Exterior algebra. --- Faithful representation. --- Finite field. --- Finite group. --- Four-dimensional space. --- Frobenius endomorphism. --- Fundamental group. --- Fundamental representation. --- Galois group. --- Gauss sum. --- Homomorphism. --- Integer. --- Irreducibility (mathematics). --- Isomorphism class. --- Kloosterman sum. --- L-function. --- Leray spectral sequence. --- Lie algebra. --- Lie theory. --- Maximal compact subgroup. --- Method of moments (statistics). --- Monodromy theorem. --- Monodromy. --- Morphism. --- Multiplicative group. --- Natural number. --- Nilpotent. --- Open problem. --- P-group. --- Pairing. --- Parameter space. --- Parameter. --- Partially ordered set. --- Perfect field. --- Point at infinity. --- Polynomial ring. --- Prime number. --- Quotient group. --- Representation ring. --- Representation theory. --- Residue field. --- Riemann hypothesis. --- Root of unity. --- Sheaf (mathematics). --- Simple Lie group. --- Skew-symmetric matrix. --- Smooth morphism. --- Special case. --- Spin representation. --- Subgroup. --- Support (mathematics). --- Symmetric matrix. --- Symplectic group. --- Symplectic vector space. --- Tensor product. --- Theorem. --- Trace (linear algebra). --- Trivial representation. --- Variable (mathematics). --- Weil conjectures. --- Weyl character formula. --- Zariski topology.