Download or read book Simple Estimation of Semiparametric Models with Measurement Errors written by Kirill S. Evdokimov and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a practical way of addressing the Errors-In-Variables (EIV) problem in the Generalized Method of Moments (GMM) framework. We focus on the settings in which the variance of the measurement errors is a fraction of that of the mismeasured variables, which is typical for empirical applications. For any initial set of moment conditions our approach provides a “corrected” set of moment conditions that do not suffer from the EIV bias. The EIV-robust estimator is then computed as a standard GMM estimator with these corrected moment conditions. We show that our estimator is √n-consistent, and that the standard tests and confidence intervals provide valid inference. This is true even when the EIV are so large that the naive estimator (that ignores the EIV problem) may have a large bias with confidence intervals having 0% coverage. Our approach requires no nonparametric estimation, which can be particularly useful when the measurement errors are multivariate, serially correlated, or non-classical.

Download or read book Large Sample Theory in a Semiparametric Partially Linear Errors in variables Models written by Hua Liang and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the partially linear model relating a response Y to predictors (X, T) with mean function XT ß + g (T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis (1994) leads to biased estimates of both the parameter ß and the function g(·) when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of ß is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed. -- Measurement Error ; Errors-in-Variables ; Functional Relations ; Non-parametric Likelihood ; Orthogonal Regression ; Partially Linear Model ; Semiparametric Models ; Structural Relations

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.

Download or read book Estimation in Semiparametric Models written by Johann Pfanzagl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.

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.

Download or read book Efficient Inference in General Semiparametric Regression Models written by Arnab Maity and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiparametric regression has become very popular in the field of Statistics over the years. While on one hand more and more sophisticated models are being developed, on the other hand the resulting theory and estimation process has become more and more involved. The main problems that are addressed in this work are related to efficient inferential procedures in general semiparametric regression problems. We first discuss efficient estimation of population-level summaries in general semiparametric regression models. Here our focus is on estimating general population-level quantities that combine the parametric and nonparametric parts of the model (e.g., population mean, probabilities, etc.). We place this problem in a general context, provide a general kernel-based methodology, and derive the asymptotic distributions of estimates of these population-level quantities, showing that in many cases the estimates are semiparametric efficient. Next, motivated from the problem of testing for genetic effects on complex traits in the presence of gene-environment interaction, we consider developing score test in general semiparametric regression problems that involves Tukey style 1 d.f form of interaction between parametrically and non-parametrically modeled covariates. We develop adjusted score statistics which are unbiased and asymptotically efficient and can be performed using standard bandwidth selection methods. In addition, to over come the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented using standard computational methods. Finally, we take up the important problem of estimation in a general semiparametric regression model when covariates are measured with an additive measurement error structure having normally distributed measurement errors. In contrast to methods that require solving integral equation of dimension the size of the covariate measured with error, we propose methodology based on Monte Carlo corrected scores to estimate the model components and investigate the asymptotic behavior of the estimates. For each of the problems, we present simulation studies to observe the performance of the proposed inferential procedures. In addition, we apply our proposed methodology to analyze nontrivial real life data sets and present the results.

Download or read book Semiparametric Identification and Estimation of Polynomial Errors In variables Models written by Jerry A. Hausman and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of Generalized Simple Measurement Error Models with Instrumental Variables written by Jeffrey Ray Thompson and published by . This book was released on 2003 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Measurement Data Modeling and Parameter Estimation written by Zhengming Wang and published by CRC Press. This book was released on 2011-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics. Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference: Introduces the basic concepts of measurements and errors Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data Covers Kalman filtering with colored noises and its applications Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors’ research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.

Download or read book Dimension Reduction in Semiparametric Measurement Error Models with Errors in Covariates written by Ronald Keith Knickerbocker and published by . This book was released on 1993 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semiparametric Estimation and Inference with Mis measured Correlated Or Mixed Observations and the Application in Ecology Medicine and Neurology written by Kun Xu and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The dissertation considers semiparametric regression models inspired by statistical problems in ecological, medical and neurological studies. In those models, the interest is usually on the estimation of a set of finite parameters with difficulties of handling some unknown distribution functions or some other unknown structures. Developing novel semiparametric treatments and deriving a class of consistent and efficient estimators can not only provide us with better inferences, but also a general framework in those studies. In capture-recapture models for closed populations, the goal is to estimate the abundance of population. When multiple error-prone measurements of a covariate are available, we discover that no suitable complete and sufficient statistic exists due to the identity between the number of captures and the number of measurements. Hence the existing treatment utilizing such statistic no longer apply. Our investigation indicates that the familiar strategy of generalized method of moments can only resolve the issue with high capture probabilities. Further complexity includes the loss of the surrogacy assumption, commonly assumed in most measurement error problems. We devise a novel semiparametric treatment to overcome those difficulties. Simulation studies and real data analysis show good performance of our method. In HIV research, we study errors-in-variables problems when the response is binary and instrumental variables are available. We construct consistent estimators through taking advantage of the prediction relation between the unobservable variables and the instruments. The asymptotic properties of the new estimator are established, and illustrated through simulation studies. We also demonstrate that the method can be readily generalized to generalized linear models and beyond. The usefulness of the method is illustrated through a real data example. Lastly, we nonparametrically estimate distribution functions for multiple populations in kin-cohort studies. The data is mixed and known to belong to a specific population with certain probabilities. Some of the observations can be further correlated, and are subject to censoring. We estimate the distributions in an optimal way through using the optimal base estimators and then combine the estimators optimally as well. The optimality implies both estimation consistency and minimum estimation variability. One obvious advantage is that our estimator does not assume any parametric forms of the distributions, and does not require to know or to model the potential correlation structure. Analysis on the Huntington's disease data is performed to illustrate the effectiveness of the method. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151746

Download or read book Semiparametric Quasilikelihood and Variance Function Estimation in Measurement Error Models written by Jungsywan H. Sepanski and published by . This book was released on 1991 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient and Adaptive Estimation for Semiparametric Models written by Peter J. Bickel and published by Springer. This book was released on 1998-06-01 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.

Download or read book On Estimation and Local Influence Analysis for Measurement Errors Models Under Heavy tailed Distributions written by V. H. Lachos and published by . This book was released on 2008 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.