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Econometrics --- Fix-point estimation --- Point estimation --- Estimation theory --- Economics, Mathematical --- Statistics --- Econometrics. --- Fix-point estimation.

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Fix-point estimation --- Estimation ponctuelle --- Netherlands --- Economic conditions --- Econometric models

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Mathematical statistics --- Econometrics --- Fix-point estimation --- Econométrie --- Estimation ponctuelle --- Point estimation --- Estimation theory --- Economics, Mathematical --- Statistics --- Econometrics. --- Fix-point estimation. --- Econométrie

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This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.

Fix-point estimation --- Equations, Roots of --- Mathematical Statistics --- Applied Mathematics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Fix-point estimation. --- Equations, Roots of. --- Roots of equations --- Point estimation --- Mathematics. --- Numerical analysis. --- Numerical Analysis. --- Mathematical analysis --- Math --- Science --- Estimation theory

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Since the publication in 1983 of Theory of Point Estimation, much new work has made it desirable to bring out a second edition. The inclusion of the new material has increased the length of the book from 500 to 600 pages; of the approximately 1000 references about 25% have appeared since 1983. The greatest change has been the addition to the sparse treatment of Bayesian inference in the first edition. This includes the addition of new sections on Equivariant, Hierarchical, and Empirical Bayes, and on their comparisons. Other major additions deal with new developments concerning the information in equality and simultaneous and shrinkage estimation. The Notes at the end of each chapter now provide not only bibliographic and historical material but also introductions to recent development in point estimation and other related topics which, for space reasons, it was not possible to include in the main text. The problem sections also have been greatly expanded. On the other hand, to save space most of the discussion in the first edition on robust estimation (in particu lar L, M, and R estimators) has been deleted. This topic is the subject of two excellent books by Hampel et al (1986) and Staudte and Sheather (1990). Other than subject matter changes, there have been some minor modifications in the presentation. .

Mathematical statistics --- Fix-point estimation --- Estimation ponctuelle --- Fix-point estimation. --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- 519.226 --- 519.2 --- #PBIB:2004.3 --- Inference and decision theory. Likelihood. Bayesian theory. Fiducial probability --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- 519.226 Inference and decision theory. Likelihood. Bayesian theory. Fiducial probability --- EPUB-LIV-FT SPRINGER-B --- Statistics. --- Applied mathematics. --- Engineering mathematics. --- Statistical Theory and Methods. --- Applications of Mathematics. --- Point estimation --- Estimation theory --- Mathematical statistics. --- Mathematics. --- Statistics . --- Engineering --- Engineering analysis --- Mathematical analysis --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistique mathématique --- Statistique mathématique --- Estimation, Théorie de l' --- Statistique bayésienne