Comparisons Between Some Estimators in Functional Errors-in-Variables Regression Models PDF Download
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Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 28
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Book Description
This report studies the functional errors-in-variables regression model. In the case of no equation error (all randomness due to measurement errors), the maximum likelihood estimator computed assuming normality is asymptotically better than the usual moments estimator, even if the errors are not normally distributed. For certain statistical problems such as randomized two group analysis of covariance, the least squares estimate is shown to be better than the aformentioned errors-in-variables methods for estimating certain important contrasts.
Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 28
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Book Description
This report studies the functional errors-in-variables regression model. In the case of no equation error (all randomness due to measurement errors), the maximum likelihood estimator computed assuming normality is asymptotically better than the usual moments estimator, even if the errors are not normally distributed. For certain statistical problems such as randomized two group analysis of covariance, the least squares estimate is shown to be better than the aformentioned errors-in-variables methods for estimating certain important contrasts.
Author: Nicholas W. Woolsey
Publisher:
ISBN:
Category :
Languages : en
Pages : 105
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Book Description
Errors-in-Variables (EIV) models are regression models in which both the explanatory and response variables are measured with error. This seemingly small change leads to a myriad of issues that are not present in the classical model. In fact, widely used methods under the classical model which are usually considered excellent become woefully inadequate. For instance, the Least Squares estimator (LS) of the slope parameter suffers from an attenuation bias while the Maximum Likelihood Estimator (MLE) of the slope parameter has infinite moments. Accordingly, several approaches have been developed in the literature in order to produce better estimators. This thesis aims to develop new estimators by undergoing a new approach. Instead of minimizing an objective function by utilizing the likelihood principle, a family of unspecified objective functions is considered. This degree of freedom allows us to develop estimators with desirable statistical properties, such as efficiency and unbiasedness up to the fourth-leading term. To derive such a weight, a general form of the second-order bias is formulated with the aid of perturbation theory. This process yields a system of first-order linear partial differential equations that yield a closed- form solution for our weight function. Accordingly, our estimator can be obtained by minimizing the objective function associated with this weight by using Levenberg-Marquardt algorithm (LM). The effectiveness and superiority of our method were assessed by a series of Monte-Carlo simulations.
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: Raymond J. Carroll
Publisher: CRC Press
ISBN: 9780412047213
Category : Mathematics
Languages : en
Pages : 334
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Book Description
This monograph provides an up-to-date discussion of analysis strategies for regression problems in which predictor variables are measured with errors. The analysis of nonlinear regression models includes generalized linear models, transform-both-sides models and quasilikelihood and variance function problems. The text concentrates on the general ideas and strategies of estimation and inference rather than being concerned with a specific problem. Measurement error occurs in many fields, such as biometry, epidemiology and economics. In particular, the book contains a large number of epidemiological examples. An outline of strategies for handling progressively more difficult problems is also provided.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 688
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Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: John P. Buonaccorsi
Publisher: CRC Press
ISBN: 1420066587
Category : Mathematics
Languages : en
Pages : 465
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Book Description
Over the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illu
Author: Raymond J. Carroll
Publisher: CRC Press
ISBN: 1420010131
Category : Mathematics
Languages : en
Pages : 484
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Book Description
It's been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and ex
Author: Odile Pons
Publisher: World Scientific
ISBN: 9814343749
Category : Mathematics
Languages : en
Pages : 210
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Book Description
This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book
Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 35
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Book Description
We consider in detail probit and logistic regression models when some of the predictors are measured with error. For normal measurement errors, the functional and structural maximum likelihood estimates (MLE) are considered; in the functional case the MLE is not generally consistent. Non-normality in the structural case is also considered. By an example and a simulation, we show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. (Author).
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
ISBN: 3642577008
Category : Mathematics
Languages : en
Pages : 210
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Book Description
In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
