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| Author | : Peisi Yan |
| Publisher | : |
| Total Pages | : 142 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
| Author | : Jaya P. N. Bishwal |
| Publisher | : Springer |
| Total Pages | : 271 |
| Release | : 2007-09-26 |
| Genre | : Mathematics |
| ISBN | : 3540744487 |
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
| Author | : George David Birkhoff |
| Publisher | : |
| Total Pages | : 48 |
| Release | : 1908 |
| Genre | : Differential equations, Linear |
| ISBN | : |
| Author | : George David Birkhoff |
| Publisher | : Sagwan Press |
| Total Pages | : 46 |
| Release | : 2015-08-22 |
| Genre | : |
| ISBN | : 9781298995223 |
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
| Author | : H. J. Bierens |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 211 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642455298 |
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.
| Author | : Raphael Abel Kasonga |
| Publisher | : National Library of Canada |
| Total Pages | : 190 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Carlos Simpson |
| Publisher | : Springer |
| Total Pages | : 144 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354046641X |
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
| Author | : Walter Rawleigh Pyper |
| Publisher | : |
| Total Pages | : 84 |
| Release | : 1970 |
| Genre | : Differential equations |
| ISBN | : |
| Author | : White Roscoe B |
| Publisher | : World Scientific |
| Total Pages | : 432 |
| Release | : 2010-08-16 |
| Genre | : Mathematics |
| ISBN | : 1911298593 |
The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
| Author | : Stanford University. Department of Statistics |
| Publisher | : |
| Total Pages | : 556 |
| Release | : 1973 |
| Genre | : Analysis of variance |
| ISBN | : |
The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood. (Modified author abstract).
