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Author: Nico J.D. Nagelkerke
Publisher: Springer Science & Business Media
ISBN: 1461228581
Category : Mathematics
Languages : en
Pages : 118
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Book Description
The theory of functional relationships concerns itself with inference from models with a more complex error structure than those existing in regression models. We are familiar with the bivariate linear relationship having measurement errors in both variables and the fact that the standard regression estimator of the slope underestimates the true slope. One complication with inference about parameters in functional relationships, is that many of the standard properties of likelihood theory do not apply, at least not in the form in which they apply to e.g. regression models. This is probably one of the reasons why these models are not adequately discussed in most general books on statistics, despite their wide applicability. In this monograph we will explore the properties of likelihood methods in the context of functional relationship models. Full and conditional likelihood methods are both considered. Possible modifications to these methods are considered when necessary. Apart from exloring the theory itself, emphasis shall be placed upon the derivation of useful estimators and their second moment properties. No attempt is made to be mathematically rigid. Proofs are usually outlined with extensive use of the Landau 0(.) and 0(.) notations. It is hoped that this shall provide more insight than the inevitably lengthy proofs meeting strict standards of mathematical rigour.
Author: Nico J.D. Nagelkerke
Publisher: Springer Science & Business Media
ISBN: 1461228581
Category : Mathematics
Languages : en
Pages : 118
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Book Description
The theory of functional relationships concerns itself with inference from models with a more complex error structure than those existing in regression models. We are familiar with the bivariate linear relationship having measurement errors in both variables and the fact that the standard regression estimator of the slope underestimates the true slope. One complication with inference about parameters in functional relationships, is that many of the standard properties of likelihood theory do not apply, at least not in the form in which they apply to e.g. regression models. This is probably one of the reasons why these models are not adequately discussed in most general books on statistics, despite their wide applicability. In this monograph we will explore the properties of likelihood methods in the context of functional relationship models. Full and conditional likelihood methods are both considered. Possible modifications to these methods are considered when necessary. Apart from exloring the theory itself, emphasis shall be placed upon the derivation of useful estimators and their second moment properties. No attempt is made to be mathematically rigid. Proofs are usually outlined with extensive use of the Landau 0(.) and 0(.) notations. It is hoped that this shall provide more insight than the inevitably lengthy proofs meeting strict standards of mathematical rigour.
Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574
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Book Description
Author: Sabine van Huffel
Publisher: SIAM
ISBN: 9780898713930
Category : Mathematics
Languages : en
Pages : 404
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Book Description
An overview of the computational issues; statistical, numerical, and algebraic properties, and new generalizations and applications of advances on TLS and EIV models. Experts from several disciplines prepared overview papers which were presented at the conference and are included in this book.
Author: I.B. MacNeill
Publisher: Springer Science & Business Media
ISBN: 9400947887
Category : Mathematics
Languages : en
Pages : 295
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Book Description
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 "camera 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.
Author: Wayne A. Fuller
Publisher: John Wiley & Sons
ISBN: 0470317337
Category : Mathematics
Languages : en
Pages : 474
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Book Description
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. "The effort of Professor Fuller is commendable . . . [the book] provides a complete treatment of an important and frequently ignored topic. Those who work with measurement error models will find it valuable. It is the fundamental book on the subject, and statisticians will benefit from adding this book to their collection or to university or departmental libraries." -Biometrics "Given the large and diverse literature on measurement error/errors-in-variables problems, Fuller's book is most welcome. Anyone with an interest in the subject should certainly have this book." -Journal of the American Statistical Association "The author is to be commended for providing a complete presentation of a very important topic. Statisticians working with measurement error problems will benefit from adding this book to their collection." -Technometrics " . . . this book is a remarkable achievement and the product of impressive top-grade scholarly work." -Journal of Applied Econometrics Measurement Error Models offers coverage of estimation for situations where the model variables are observed subject to measurement error. Regression models are included with errors in the variables, latent variable models, and factor models. Results from several areas of application are discussed, including recent results for nonlinear models and for models with unequal variances. The estimation of true values for the fixed model, prediction of true values under the random model, model checks, and the analysis of residuals are addressed, and in addition, procedures are illustrated with data drawn from nearly twenty real data sets.
Author: George A. F. Seber
Publisher: John Wiley & Sons
ISBN: 0471725307
Category : Mathematics
Languages : en
Pages : 800
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Book Description
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
Author: Philip J. Brown
Publisher: American Mathematical Soc.
ISBN: 0821851179
Category : Mathematics
Languages : en
Pages : 262
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Book Description
Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. This book treats general aspects of the measurement problem and features a discussion of the history of measurement error models.
Author: Santner
Publisher: CRC Press
ISBN: 9780824772741
Category : Technology & Engineering
Languages : en
Pages : 336
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Book Description
Multiple comparisons; Selection and ranking; Estimation and testing.
Author: Biswa Nath Datta
Publisher: SIAM
ISBN: 9780898712230
Category : Technology & Engineering
Languages : en
Pages : 692
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Book Description
Author: Brian L. Joiner
Publisher:
ISBN:
Category : Annals of mathematical statistics
Languages : en
Pages : 512
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Book Description
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
