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Application And Computation Of Likelihood Methods For Regression With Measurement Error
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Book Synopsis Application and Computation of Likelihood Methods for Regression with Measurement Error by : Roger Higdon
Download or read book Application and Computation of Likelihood Methods for Regression with Measurement Error written by Roger Higdon and published by . This book was released on 1998 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis advocates the use of maximum likelihood analysis for generalized regression models with measurement error in a single explanatory variable. This will be done first by presenting a computational algorithm and the numerical details for carrying out this algorithm on a wide variety of models. The computational methods will be based on the EM algorithm in conjunction with the use of Gauss-Hermite quadrature to approximate integrals in the E-step. Second, this thesis will demonstrate the relative superiority of likelihood-ratio tests and confidence intervals over those based on asymptotic normality of estimates and standard errors, and that likelihood methods may be more robust in these situations than previously thought. The ability to carry out likelihood analysis under a wide range of distributional assumptions, along with the advantages of likelihood ratio inference and the encouraging robustness results make likelihood analysis a practical option worth considering in regression problems with explanatory variable measurement error.
Book Synopsis Statistical Analysis of Measurement Error Models and Applications by : Philip J. Brown
Download or read book Statistical Analysis of Measurement Error Models and Applications written by Philip J. Brown and published by American Mathematical Soc.. This book was released on 1990-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. Examples include linear and nonlinear errors-in-variables regression models, calibration and inverse regression models, factor analysis models, latent structure models, and simultaneous equations models. Such models are used in a wide variety of areas, including medicine, the life sciences, econometrics, chemometrics, geology, sample surveys, and time series. Although the problem of estimating the parameters of such models exists in most scientific fields, there is a need for more sources that treat measurement error models as an area of statistical methodology. This volume is designed to address that need. This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Statistical Analysis of Measurement Error Models and Applications. The conference was held at Humboldt State University in Arcata, California in June 1989. The papers in this volume fall into four broad groups. The first group treats general aspects of the measurement problem and features a discussion of the history of measurement error models. The second group focuses on inference for the nonlinear measurement error model, an active area of research which generated considerable interest at the conference. The third group of papers examines computational aspects of estimation, while the final set studies estimators possessing robustness properties against deviations from common model assumptions.
Book Synopsis Measurement Error by : John P. Buonaccorsi
Download or read book Measurement Error written by John P. Buonaccorsi and published by CRC Press. This book was released on 2010-03-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Maximum Likelihood Computations for Regression with Measurement Error by : Roger Higdon
Download or read book Maximum Likelihood Computations for Regression with Measurement Error written by Roger Higdon and published by . This book was released on 1998 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Radiation Risk Estimation by : Sergii Masiuk
Download or read book Radiation Risk Estimation written by Sergii Masiuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure doses Overview of risk models realized in program package EPICURE Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident Elements of estimating equations theory Consistency of efficient methods Efficient SIMEX method as a combination of the SIMEX method and the corrected score method Application of regression calibration in the model with additive error in exposure doses
Book Synopsis Regression Models for the Comparison of Measurement Methods by : Heleno Bolfarine
Download or read book Regression Models for the Comparison of Measurement Methods written by Heleno Bolfarine and published by Springer Nature. This book was released on 2020-10-27 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an updated account of the regression techniques employed in comparing analytical methods and to test the biases of one method relative to others – a problem commonly found in fields like analytical chemistry, biology, engineering, and medicine. Methods comparison involves a non-standard regression problem; when a method is to be tested in a laboratory, it may be used on samples of suitable reference material, but frequently it is used with other methods on a range of suitable materials whose concentration levels are not known precisely. By presenting a sound statistical background not found in other books for the type of problem addressed, this book complements and extends topics discussed in the current literature. It highlights the applications of the presented techniques with the support of computer routines implemented using the R language, with examples worked out step-by-step. This book is a valuable resource for applied statisticians, practitioners, laboratory scientists, geostatisticians, process engineers, geologists and graduate students.
Book Synopsis Semiparametric Maximum Likelihood for Regression with Measurement Error by : Eun-Young Suh
Download or read book Semiparametric Maximum Likelihood for Regression with Measurement Error written by Eun-Young Suh and published by . This book was released on 2001 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiparametric maximum likelihood analysis allows inference in errors-invariables models with small loss of efficiency relative to full likelihood analysis but with significantly weakened assumptions. In addition, since no distributional assumptions are made for the nuisance parameters, the analysis more nearly parallels that for usual regression. These highly desirable features and the high degree of modelling flexibility permitted warrant the development of the approach for routine use. This thesis does so for the special cases of linear and nonlinear regression with measurement errors in one explanatory variable. A transparent and flexible computational approach is developed, the analysis is exhibited on some examples, and finite sample properties of estimates, approximate standard errors, and likelihood ratio inference are clarified with simulation.
Book Synopsis Local Regression and Likelihood by : Clive Loader
Download or read book Local Regression and Likelihood written by Clive Loader and published by Springer Science & Business Media. This book was released on 2006-05-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.
Book Synopsis Maximum Likelihood Estimation of Measurement Error Models Based on the Monte Carlo EM Algorithm by : Antara Majumdar
Download or read book Maximum Likelihood Estimation of Measurement Error Models Based on the Monte Carlo EM Algorithm written by Antara Majumdar and published by . This book was released on 2007 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Likelihood based estimation of stochastic models when one of the explanatory variables is masked by measurement error, is presented. Special methods are required to estimate the parameters of a model with one or more explanatory variables that are measured with error. In such models, the variable measured with error is unobservable. Only an unbiased manifestation is observable. The method proposed, provides an adjustment to obtain unbiased estimates of model parameters. The correction of bias, however, is not possible without additional identifying information. An instrumental variable is a practical form of additional information that can be used for this purpose. By treating the unobservable explanatory variable as 'missing' data the Markov Chain Monte Carlo Expectation Maximization (MCEM) algorithm is applied for maximum likelihood estimation of the parameters of a measurement error model with identifying information in the form of an instrumental variable. Implementation strategies, computational aspects, behavior of the estimators and inference resulting from application of the MCEM algorithm to the instrumental variable measurement error model are studied. A general methodology is developed that encompasses a variety of previously studied special case models and it is shown how they all can be modeled and estimated using the MCEM algorithm. Through our method it is shown how a structural logistic regression measurement error model can be directly fitted without the probit approximation. This was not possible prior to the research presented in this dissertation. The proposed methodology is compared numerically with the exact maximum likelihood estimates for two normal family models. Also, the behavior of the method is investigated when one of the variance parameters is near the boundary of the parameter space. The problem of measurement error in a survival time model with right censoring is considered and it is shown how the proposed method can be used to estimate a hazard function model, by construction of some special likelihoods and further methodological development. Two methods have been proposed, one of which is a semi-parametric method and the other is full parametric.
Book Synopsis Handbook of Measurement Error Models by : Grace Y. Yi
Download or read book Handbook of Measurement Error Models written by Grace Y. Yi and published by CRC Press. This book was released on 2021-09-28 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error arises ubiquitously in applications and has been of long-standing concern in a variety of fields, including medical research, epidemiological studies, economics, environmental studies, and survey research. While several research monographs are available to summarize methods and strategies of handling different measurement error problems, research in this area continues to attract extensive attention. The Handbook of Measurement Error Models provides overviews of various topics on measurement error problems. It collects carefully edited chapters concerning issues of measurement error and evolving statistical methods, with a good balance of methodology and applications. It is prepared for readers who wish to start research and gain insights into challenges, methods, and applications related to error-prone data. It also serves as a reference text on statistical methods and applications pertinent to measurement error models, for researchers and data analysts alike. Features: Provides an account of past development and modern advancement concerning measurement error problems Highlights the challenges induced by error-contaminated data Introduces off-the-shelf methods for mitigating deleterious impacts of measurement error Describes state-of-the-art strategies for conducting in-depth research
Book Synopsis Aspects of Misspecification in Statistical Models by : Wenxin Jiang
Download or read book Aspects of Misspecification in Statistical Models written by Wenxin Jiang and published by . This book was released on 1996 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Poisson Regression with Laplace Measurement Error by : Shengnan Chen
Download or read book Poisson Regression with Laplace Measurement Error written by Shengnan Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, novel estimation procedures are proposed for a class of Poisson linear regression when the covariate is contaminated with Laplace measurement error. This dissertation contains two research projects. In the first project, we propose a weighted least squares estimation procedure that incorporates the first two conditional moments of the response variable given the observed surrogate, and the weight function is intentionally chosen to avoid the complexity caused by the random denominator and to increase the estimation efficiency. To solve for the conditional moments, a Tweedie-type formula for the conditional expectation of the likelihood function given the observed surrogate has been adopted. Instead of assuming the distribution of the unobserved covariate is known, we assume that the distribution of that latent variable is unknown. Large sample properties of the proposed estimator, including the consistency and the asymptotic normality, are discussed. The finite sample performance of the proposed estimation procedure is evaluated by simulation studies, showing that the proposed estimator is more efficient than the existing ones. In the second project, we propose a corrected maximum likelihood estimation procedure based upon the Tweedie-type formula. Two situations, the distribution of the latent variable is known as well as unknown, are considered. Large sample properties of the proposed estimator are discussed, and simulation study shows that the estimator is more efficient than the existing estimation procedures. Besides, further simulation studies are also conducted to compare our proposed two estimation procedures. And sensitivity analysis has been done to examine the robustness of our methods in real data. Although the discussion is conducted for univariate cases, the proposed estimation procedure can be readily extended to the multivariate cases by using multivariate Tweedie-type formulae.
Book Synopsis Regression Diagnostics by : John Fox
Download or read book Regression Diagnostics written by John Fox and published by SAGE Publications. This book was released on 2019-12-09 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression diagnostics are methods for determining whether a regression model that has been fit to data adequately represents the structure of the data. For example, if the model assumes a linear (straight-line) relationship between the response and an explanatory variable, is the assumption of linearity warranted? Regression diagnostics not only reveal deficiencies in a regression model that has been fit to data but in many instances may suggest how the model can be improved. The Second Edition of this bestselling volume by John Fox considers two important classes of regression models: the normal linear regression model (LM), in which the response variable is quantitative and assumed to have a normal distribution conditional on the values of the explanatory variables; and generalized linear models (GLMs) in which the conditional distribution of the response variable is a member of an exponential family. R code and data sets for examples within the text can be found on an accompanying website.
Book Synopsis Measurement Error and Misclassification in Statistics and Epidemiology by : Paul Gustafson
Download or read book Measurement Error and Misclassification in Statistics and Epidemiology written by Paul Gustafson and published by CRC Press. This book was released on 2003-09-25 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mismeasurement of explanatory variables is a common hazard when using statistical modeling techniques, and particularly so in fields such as biostatistics and epidemiology where perceived risk factors cannot always be measured accurately. With this perspective and a focus on both continuous and categorical variables, Measurement Error and Misclassi
Book Synopsis Econometrics in Theory and Practice by : Robert Galata
Download or read book Econometrics in Theory and Practice written by Robert Galata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 9
Book Synopsis Time Series Analysis: Methods and Applications by : Tata Subba Rao
Download or read book Time Series Analysis: Methods and Applications written by Tata Subba Rao and published by Elsevier. This book was released on 2012-06-26 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Handbook of Statistics' is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with volume 30 dealing with time series.
Book Synopsis Bayesian Regression Modeling with INLA by : Xiaofeng Wang
Download or read book Bayesian Regression Modeling with INLA written by Xiaofeng Wang and published by CRC Press. This book was released on 2018-01-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work. Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.
