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Asymptotic Theory Of Nonlinear Regression

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Asymptotic Theory Of Nonlinear Regression

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Author : A. A. Ivanov
language : en
Publisher:
Release Date : 2014-01-15

Asymptotic Theory Of Nonlinear Regression written by A. A. Ivanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Asymptotic Theory Of Nonlinear Regression

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Author : A.A. Ivanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Asymptotic Theory Of Nonlinear Regression written by A.A. Ivanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().

Asymptotic Theory Of Nonlinear Regression

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Author : A. V. Ivanov
language : en
Publisher: Springer
Release Date : 1997

Asymptotic Theory Of Nonlinear Regression written by A. V. Ivanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Language Arts & Disciplines categories.

This book presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. It is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section. The volume concludes with an extensive Bibliography. Audience: This book will be of interest to mathematicians and statisticians whose work involves stochastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.

Nonlinear Regression

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Author : George A. F. Seber
language : en
Publisher: John Wiley & Sons
Release Date : 2005-02-25

Nonlinear Regression written by George A. F. Seber and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-25 with Mathematics categories.

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of Nonlinear Regression "A very good book and an important one in that it is likely to become a standard reference for all interested in nonlinear regression; and I would imagine that any statistician concerned with nonlinear regression would want a copy on his shelves." –The Statistician "Nonlinear Regression also includes a reference list of over 700 entries. The compilation of this material and cross-referencing of it is one of the most valuable aspects of the book. Nonlinear Regression can provide the researcher unfamiliar with a particular specialty area of nonlinear regression an introduction to that area of nonlinear regression and access to the appropriate references . . . Nonlinear Regression provides by far the broadest discussion of nonlinear regression models currently available and will be a valuable addition to the library of anyone interested in understanding and using such models including the statistical researcher." –Mathematical Reviews

Robust Methods And Asymptotic Theory In Nonlinear Econometrics

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Author : H. J. Bierens
language : en
Publisher: Springer
Release Date : 2012-03-02

Robust Methods And Asymptotic Theory In Nonlinear Econometrics written by H. J. Bierens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-02 with Mathematics categories.

This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate if the distributions of both the errors and the regressors have fat tails. This study also improves and extends the NL2SLSE theory of Amemiya. The method involved is a variant of the instrumental variables method, requiring at least as many instrumental variables as parameters to be estimated. The new MIE method requires less instrumental variables. Asymptotic normality can be derived by employing only one instrumental variable and consistency can even be proved with out using any instrumental variables at all.

Asymptotic Theory Of Statistical Inference For Time Series

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Author : Masanobu Taniguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Asymptotic Theory Of Statistical Inference For Time Series written by Masanobu Taniguchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

There has been much demand for the statistical analysis of dependent ob servations in many fields, for example, economics, engineering and the nat ural sciences. A model that describes the probability structure of a se ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.

Robust Methods And Asymptotic Theory In Nonlinear Econometrics

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Author : Herman J. Bierens
language : en
Publisher: Springer
Release Date : 1981

Robust Methods And Asymptotic Theory In Nonlinear Econometrics written by Herman J. Bierens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Business & Economics categories.

Nonlinear Regression Analysis And Its Applications

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Author : Douglas M. Bates
language : en
Publisher: Wiley-Interscience
Release Date : 2007-04-23

Nonlinear Regression Analysis And Its Applications written by Douglas M. Bates and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-23 with Mathematics categories.

Provides a presentation of the theoretical, practical, and computational aspects of nonlinear regression. There is background material on linear regression, including a geometrical development for linear and nonlinear least squares.

Model Discrimination For Nonlinear Regression Models

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Author : Dale S. Borowiak
language : en
Publisher: CRC Press
Release Date : 2020-11-26

Model Discrimination For Nonlinear Regression Models written by Dale S. Borowiak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.

Borowiak (math, U. of Akron) discusses model discrimination based upon incorrect selection probability, presents diagnostic statistics and formal hypothesis test procedures to assess a model's fit and stability, explains the use of computer computations such as the jackknife and bootstrap, and demon

Optimal Design And Related Areas In Optimization And Statistics

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Author : Luc Pronzato
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-25

Optimal Design And Related Areas In Optimization And Statistics written by Luc Pronzato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-25 with Mathematics categories.

The present volume is a collective monograph devoted to applications of the optimal design theory in optimization and statistics. The chapters re?ect the topics discussed at the workshop “W-Optimum Design and Related Statistical Issues” that took place in Juan-les-Pins, France, in May 2005. The title of the workshop was chosen as a light-hearted celebration of the work of Henry Wynn. It was supported by the Laboratoire I3S (CNRS/Universit ́ e de Nice, Sophia Antipolis), to which Henry is a frequent visitor. The topics covered partly re?ect the wide spectrum of Henry’s research - terests. Algorithms for constructing optimal designs are discussed in Chap. 1, where Henry’s contribution to the ?eld is acknowledged. Steepest-ascent - gorithms used to construct optimal designs are very much related to general gradientalgorithmsforconvexoptimization. Inthelasttenyears,asigni?cant part of Henry’s research was devoted to the study of the asymptotic prop- ties of such algorithms. This topic is covered by Chaps. 2 and 3. The work by Alessandra Giovagnoli concentrates on the use of majorization and stoch- tic ordering, and Chap. 4 is a hopeful renewal of their collaboration. One of Henry’s major recent interests is what is now called algebraic statistics, the application of computational commutative algebra to statistics, and he was partly responsible for introducing the experimental design sub-area, reviewed in Chap. 5. One other sub-area is the application to Bayesian networks and Chap. 6 covers this, with Chap. 7 being strongly related.

Asymptotic Theory Of Nonlinear Regression

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