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Semiparametric Maximum Likelihood For Regression With Measurement Error
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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 Semiparametric Regression by : David Ruppert
Download or read book Semiparametric Regression written by David Ruppert and published by Cambridge University Press. This book was released on 2003-07-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even experts on semiparametric regression should find something new here.
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 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 Semiparametric Regression with Kernel Error Model by : Ao Yuan
Download or read book Semiparametric Regression with Kernel Error Model written by Ao Yuan and published by . This book was released on 2006 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Work of Raymond J. Carroll by : Marie Davidian
Download or read book The Work of Raymond J. Carroll written by Marie Davidian and published by Springer. This book was released on 2014-06-06 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Raymond J. Carroll's research and commentary on its impact by leading statisticians. Each of the seven main parts focuses on a key research area: Measurement Error, Transformation and Weighting, Epidemiology, Nonparametric and Semiparametric Regression for Independent Data, Nonparametric and Semiparametric Regression for Dependent Data, Robustness, and other work. The seven subject areas reviewed in this book were chosen by Ray himself, as were the articles representing each area. The commentaries not only review Ray’s work, but are also filled with history and anecdotes. Raymond J. Carroll’s impact on statistics and numerous other fields of science is far-reaching. His vast catalog of work spans from fundamental contributions to statistical theory to innovative methodological development and new insights in disciplinary science. From the outset of his career, rather than taking the “safe” route of pursuing incremental advances, Ray has focused on tackling the most important challenges. In doing so, it is fair to say that he has defined a host of statistics areas, including weighting and transformation in regression, measurement error modeling, quantitative methods for nutritional epidemiology and non- and semiparametric regression.
Book Synopsis Statistical Analysis with Measurement Error or Misclassification by : Grace Y. Yi
Download or read book Statistical Analysis with Measurement Error or Misclassification written by Grace Y. Yi and published by Springer. This book was released on 2017-08-02 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on measurement error and misclassification covers a broad range of problems and emphasizes unique features in modeling and analyzing problems arising from medical research and epidemiological studies. Many measurement error and misclassification problems have been addressed in various fields over the years as well as with a wide spectrum of data, including event history data (such as survival data and recurrent event data), correlated data (such as longitudinal data and clustered data), multi-state event data, and data arising from case-control studies. Statistical Analysis with Measurement Error or Misclassification: Strategy, Method and Application brings together assorted methods in a single text and provides an update of recent developments for a variety of settings. Measurement error effects and strategies of handling mismeasurement for different models are closely examined in combination with applications to specific problems. Readers with diverse backgrounds and objectives can utilize this text. Familiarity with inference methods—such as likelihood and estimating function theory—or modeling schemes in varying settings—such as survival analysis and longitudinal data analysis—can result in a full appreciation of the material, but it is not essential since each chapter provides basic inference frameworks and background information on an individual topic to ease the access of the material. The text is presented in a coherent and self-contained manner and highlights the essence of commonly used modeling and inference methods. This text can serve as a reference book for researchers interested in statistical methodology for handling data with measurement error or misclassification; as a textbook for graduate students, especially for those majoring in statistics and biostatistics; or as a book for applied statisticians whose interest focuses on analysis of error-contaminated data. Grace Y. Yi is Professor of Statistics and University Research Chair at the University of Waterloo. She is the 2010 winner of the CRM-SSC Prize, an honor awarded in recognition of a statistical scientist's professional accomplishments in research during the first 15 years after having received a doctorate. She is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute.
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 Efficient Semiparametric Estimators for Biological, Genetic, and Measurement Error Applications by : Tanya Garcia
Download or read book Efficient Semiparametric Estimators for Biological, Genetic, and Measurement Error Applications written by Tanya Garcia and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many statistical models, like measurement error models, a general class of survival models, and a mixture data model with random censoring, are semiparametric where interest lies in estimating finite-dimensional parameters in the presence of infinite-dimensional nuisance parameters. Developing efficient estimators for the parameters of interest in these models is important because such estimators provide better inferences. For a general regression model with measurement error, we utilize semiparametric theory to develop an unprecedented estimation procedure which delivers consistent estimators even when the model error and latent variable distributions are misspecified. Until now, root-n consistent estimators for this setting were not attainable except for special cases, like a polynomial relationship between the response and mismeasured variables. Through simulation studies and a nutrition study application, we demonstrate that our method outperforms existing methods which ignore measurement error or require a correct model error distribution. In randomized clinical trials, scientists often compare two-sample survival data with a log-rank test. The two groups typically have nonproportional hazards, however, and using a log rank test results in substantial power loss. To ameliorate this issue and improve model efficiency, we propose a model-free strategy of incorporating auxiliary covariates in a general class of survival models. Our approach produces an unbiased, asymptotically normal estimator with significant efficiency gains over current methods. Lastly, we apply semiparametric theory to mixture data models common in kin-cohort designs of Huntington's disease where interest lies in comparing the estimated age-at-death distributions for disease gene carriers and non-carriers. The distribution of the observed, possibly censored, outcome is a mixture of the genotype-specific distributions where the mixing proportions are computed based on the genotypes which are independent of the trait outcomes. Current methods for such data include a Cox proportional hazards model which is susceptible to model misspecification, and two types of nonparametric maximum likelihood estimators which are either inefficient or inconsistent. Using semiparametric theory, we propose an inverse probability weighting estimator (IPW), a nonparametrically imputed estimator and an optimal augmented IPW estimator which provide more reasonable estimates for the age-at-death distributions, and are not susceptible to model misspecification nor poor efficiencies.
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 Regression Calibration and Maximum Likelihood Inference for Measurement Error Models by : Vicente J. Monleon-Moscardo
Download or read book Regression Calibration and Maximum Likelihood Inference for Measurement Error Models written by Vicente J. Monleon-Moscardo and published by . This book was released on 2005 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression calibration inference seeks to estimate regression models with measurement error in explanatory variables by replacing the mismeasured variable by its conditional expectation, given a surrogate variable, in an estimation procedure that would have been used if the true variable were available. This study examines the effect of the uncertainty in the estimation of the required conditional expectation on inference about regression parameters, when the true explanatory variable and its surrogate are observed in a calibration dataset and related through a normal linear model. The exact sampling distribution of the regression calibration estimator is derived for normal linear regression when independent calibration data are available. The sampling distribution is skewed and its moments are not defined, but its median is the parameter of interest. It is shown that, when all random variables are normally distributed, the regression calibration estimator is equivalent to maximum likelihood provided a natural estimate of variance is non-negative. A check for this equivalence is useful in practice for judging the suitability of regression calibration. Results about relative efficiency are provided for both external and internal calibration data. In some cases maximum likelihood is substantially more efficient than regression calibration. In general, though, a more important concern when the necessary conditional expectation is uncertain, is that inferences based on approximate normality and estimated standard errors may be misleading. Bootstrap and likelihood-ratio inferences are preferable.
Book Synopsis Semiparametric Maximum Likelihood Estimation of Nonlinear Regression Models and GARCH Models by :
Download or read book Semiparametric Maximum Likelihood Estimation of Nonlinear Regression Models and GARCH Models written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Semiparametric Regression Estimation Using Targeted Maximum Likelihood with Application to Biomarker Discovery and Epidemiology by : Catherine Ann Tuglus
Download or read book Robust Semiparametric Regression Estimation Using Targeted Maximum Likelihood with Application to Biomarker Discovery and Epidemiology written by Catherine Ann Tuglus and published by . This book was released on 2010 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many scientific studies the goal is to determine the effect of a particular feature or variable on a given outcome in order to help understand, identify, and quantify the driving factors behind a particular phenomena. This type of analysis is commonly referred to as variable importance analysis. Parametric methods used to estimate these effects are prone to bias. This bias is often the result of incorrect model specification and improper inference for the parameter of interest. Alternative machine learning techniques, such as Random Forest, often result in abstract measures of importance whose inference depends on a computationally intensive bootstrap analysis. In this thesis, robust estimators for variable importance based on targeted maximum likelihood methodology are presented and developed for three types of outcomes (1) univariate continuous, (2) multivariate continuous, and (3) binary outcome. These estimators are specifically designed to target the effect of a variable of interest on an outcome while adjusting for confounders when the variable of interest is of general form (i.e. continuous or discrete). When the outcome is continuous (1,2), the effect is on an additive scale. When the outcome is binary (3), the effect is on a multiplicative scale, and the importance measure is a relative risk. The estimators are developed under a flexible semiparametric model, in which only components related to the variable of interest must be fully specified, and effect modification can be easily incorporated. Based on targeted maximum likelihood theory, the presented estimators are double robust and locally efficient, and correct inference for the parameter of interest is available using the corresponding influence curve. In this thesis, the three estimators relating to the three outcomes are derived from targeted maximum likelihood methodology and implemented by adapting standard statistical regression software. These estimators are applied in both simulation and application. In a simulated biomarker discovery analysis, the robustness of the estimator for a univariate continuous outcome is compared to other common methods of variable importance under increasing correlation among the covariates. In a repeated measures setting, the double robust property of the estimator for a multivariate continuous outcome is demonstrated in simulation, and the estimator is applied in a transcription factor analysis to determine the activity level of transcription factors during the cell cycle in yeast. For a binary outcome, the estimator for the relative risk is applied to estimate the effect of HIV genetic susceptibility scores on viral response. Effect modification is also explored and model selection methodology is introduced.
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 Semiparametric Estimation in Logistic Measurement Error Models by : Raymond J. Carroll
Download or read book Semiparametric Estimation in Logistic Measurement Error Models written by Raymond J. Carroll and published by . This book was released on 1989 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional assumptions are made about the true predictor or its surrogate. We develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible. The estimate relies on kernel regression techniques. For scalar predictors, by a detailed analysis of the mean-squared error of the parameter estimate, we obtain a representation for an optimal bandwidth.
Book Synopsis Parameter Estimation in Nonlinear Regression with Covariate Measurement Error by : Mary Margaret Dowling
Download or read book Parameter Estimation in Nonlinear Regression with Covariate Measurement Error written by Mary Margaret Dowling and published by . This book was released on 1991 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Epidemiology by : Wolfgang Ahrens
Download or read book Handbook of Epidemiology written by Wolfgang Ahrens and published by Springer Science & Business Media. This book was released on 2007-07-26 with total page 1628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Epidemiology provides a comprehensive overview of the field and thus bridges the gap between standard textbooks of epidemiology and dispersed publications for specialists that have a narrowed focus on specific areas. It reviews the key issues and methodological approaches pertinent to the field for which the reader pursues an expatiated overview. It thus serves both as a first orientation for the interested reader and as a starting point for an in-depth study of a specific area, as well as a quick reference and recapitulatory overview for the expert. The book includes topics that are usually missing in standard textbooks.
