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Asymptotic Properties Of Nonlinear Least Squares Estimates In Stochastic Regression Models
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Book Synopsis Robust Methods and Asymptotic Theory in Nonlinear Econometrics by : H. J. Bierens
Download or read book Robust Methods and Asymptotic Theory in Nonlinear Econometrics written by H. J. Bierens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Design of Experiments in Nonlinear Models by : Luc Pronzato
Download or read book Design of Experiments in Nonlinear Models written by Luc Pronzato and published by Springer Science & Business Media. This book was released on 2013-04-10 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments. The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter. Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. A survey of algorithmic methods for the construction of optimal designs is provided.
Book Synopsis Regression Analysis Under A Priori Parameter Restrictions by : Pavel S. Knopov
Download or read book Regression Analysis Under A Priori Parameter Restrictions written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2011-09-28 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance
Book Synopsis Dynamic Nonlinear Econometric Models by : Benedikt M. Pötscher
Download or read book Dynamic Nonlinear Econometric Models written by Benedikt M. Pötscher and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many relationships in economics, and also in other fields, are both dynamic and nonlinear. A major advance in econometrics over the last fifteen years has been the development of a theory of estimation and inference for dy namic nonlinear models. This advance was accompanied by improvements in computer technology that facilitate the practical implementation of such estimation methods. In two articles in Econometric Reviews, i.e., Pötscher and Prucha {1991a,b), we provided -an expository discussion of the basic structure of the asymptotic theory of M-estimators in dynamic nonlinear models and a review of the literature up to the beginning of this decade. Among others, the class of M-estimators contains least mean distance estimators (includ ing maximum likelihood estimators) and generalized method of moment estimators. The present book expands and revises the discussion in those articles. It is geared towards the professional econometrician or statistician. Besides reviewing the literature we also presented in the above men tioned articles a number of then new results. One example is a consis tency result for the case where the identifiable uniqueness condition fails.
Book Synopsis Selected Works of David Brillinger by : Peter Guttorp
Download or read book Selected Works of David Brillinger written by Peter Guttorp and published by Springer Science & Business Media. This book was released on 2013-04-10 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 30 of David Brillinger's most influential papers. He is an eminent statistical scientist, having published broadly in time series and point process analysis, seismology, neurophysiology, and population biology. Each of these areas are well represented in the book. The volume has been divided into four parts, each with comments by one of Dr. Brillinger's former PhD students. His more theoretical papers have comments by Victor Panaretos from Switzerland. The area of time series has commentary by Pedro Morettin from Brazil. The biologically oriented papers are commented by Tore Schweder from Norway and Haiganoush Preisler from USA, while the point process papers have comments by Peter Guttorp from USA. In addition, the volume contains a Statistical Science interview with Dr. Brillinger, and his bibliography.
Book Synopsis Empirical Estimates in Stochastic Optimization and Identification by : Pavel S. Knopov
Download or read book Empirical Estimates in Stochastic Optimization and Identification written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains problems of stochastic optimization and identification. Results concerning uniform law of large numbers, convergence of approximate estimates of extreme points, as well as empirical estimates of functionals with probability 1 and in probability are presented. Audience: Specialists in stochastic optimization and estimations, postgraduate students, and graduate students studying such topics
Book Synopsis Asymptotic Theory of Nonlinear Regression by : A.A. Ivanov
Download or read book Asymptotic Theory of Nonlinear Regression written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ().
Book Synopsis Advances in the Statistical Sciences: Applied Probability, Stochastic Processes, and Sampling Theory by : I.B. MacNeill
Download or read book Advances in the Statistical Sciences: Applied Probability, Stochastic Processes, and Sampling Theory written by I.B. MacNeill and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 27-31, 1985, a series of symposia was held at The University of Western Ontario, London, Canada, to celebrate the 70th birthday of Pro fessor V. M. Joshi. These symposia were chosen to reflect Professor Joshi's research interests as well as areas of expertise in statistical science among faculty in the Departments of Statistical and Actuarial Sciences, Economics, Epidemiology and Biostatistics, and Philosophy. From these symposia, the six volumes which comprise the "Joshi Festschrift" have arisen. The 117 articles in this work reflect the broad interests and high quality of research of those who attended our conference. We would like to thank all of the contributors for their superb cooperation in helping us to complete this project. Our deepest gratitude must go to the three people who have spent so much of their time in the past year typing these volumes: Jackie Bell, Lise Constant, and Sandy Tarnowski. This work has been printed from "carnera ready" copy produced by our Vax 785 computer and QMS Lasergraphix printers, using the text processing software TEX. At the initiation of this project, we were neophytes in the use of this system. Thank you, Jackie, Lise, and Sandy, for having the persistence and dedication needed to complete this undertaking.
Book Synopsis Advanced Methods in Statistics, Data Science and Related Applications by : Matilde Bini
Download or read book Advanced Methods in Statistics, Data Science and Related Applications written by Matilde Bini and published by Springer Nature. This book was released on with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Theory of Nonlinear Regression by : A. V. Ivanov
Download or read book Asymptotic Theory of Nonlinear Regression written by A. V. Ivanov and published by Springer. This book was released on 1997 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series by : K. Dzhaparidze
Download or read book Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series written by K. Dzhaparidze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Longitudinal and Panel Data by : Edward W. Frees
Download or read book Longitudinal and Panel Data written by Edward W. Frees and published by Cambridge University Press. This book was released on 2004-08-16 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to foundations and applications for quantitatively oriented graduate social-science students and individual researchers.
Book Synopsis Random Iterative Models by : Marie Duflo
Download or read book Random Iterative Models written by Marie Duflo and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, self-contained review of a wide range of recursive methods for stabilization, identification and control of complex stochastic models (guiding a rocket or a plane, organizing multi-access broadcast channels, self-learning of neural networks ...). Suitable for mathematicians (researchers and also students) and engineers.
Book Synopsis Nonparametric and Semiparametric Methods in Econometrics and Statistics by : William A. Barnett
Download or read book Nonparametric and Semiparametric Methods in Econometrics and Statistics written by William A. Barnett and published by Cambridge University Press. This book was released on 1991-06-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a 1988 symposium on the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data.
Book Synopsis Nonlinear Econometric Modeling in Time Series by : William A. Barnett
Download or read book Nonlinear Econometric Modeling in Time Series written by William A. Barnett and published by Cambridge University Press. This book was released on 2000-05-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the more recent developments in nonlinear time series, including Bayesian analysis and cointegration tests.
Book Synopsis Short-Memory Linear Processes and Econometric Applications by : Kairat T. Mynbaev
Download or read book Short-Memory Linear Processes and Econometric Applications written by Kairat T. Mynbaev and published by John Wiley & Sons. This book was released on 2011-05-23 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins with central limit theorems (CLTs) for weighted sums of short memory linear processes. This part contains the analysis of certain operators in Lp spaces and their employment in the derivation of CLTs. The applications of CLTs are to the asymptotic distribution of various estimators for several econometric models. Among the models discussed are static linear models with slowly varying regressors, spatial models, time series autoregressions, and two nonlinear models (binary logit model and nonlinear model whose linearization contains slowly varying regressors). The estimation procedures include ordinary and nonlinear least squares, maximum likelihood, and method of moments. Additional topical coverage includes an introduction to operators, probabilities, and linear models; Lp-approximable sequences of vectors; convergence of linear and quadratic forms; regressions with slowly varying regressors; spatial models; convergence; nonlinear models; and tools for vector autoregressions.
