Download or read book Semiparametric Efficient and Inefficient Estimation for the Auxiliary Outcome Problem with the Conditional Mean Model written by Jinbo Chen and published by . This book was released on 2002 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficiency Bounds for Missing Data Models with Semiparametric Restrictions written by Bryan S. Graham and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random (MAR) coincides with that of a particular augmented moment condition problem. The augmented system consists of the inverse probability weighted (IPW) original moment restriction and an additional conditional moment restriction which exhausts all other implications of the MAR assumption. The paper also investigates the value of additional semiparametric restrictions on the conditional expectation function (CEF) of the original moment function given always- observed covariates. In the program evaluation context, for example, such restrictions are implied by semiparametric models for the potential outcome CEFs given baseline covariates. The efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem. Some implications of these results for estimation are briefly discussed.

Download or read book New Developments in Biostatistics and Bioinformatics written by Jianqing Fan and published by World Scientific. This book was released on 2009 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an overview of recent developments in biostatistics and bioinformatics. Written by active researchers in these emerging areas, it is intended to give graduate students and new researchers an idea of where the frontiers of biostatistics and bioinformatics are as well as a forum to learn common techniques in use, so that they can advance the fields via developing new techniques and new results. Extensive references are provided so that researchers can follow the threads to learn more comprehensively what the literature is and to conduct their own research. In particulars, the book covers three important and rapidly advancing topics in biostatistics: analysis of survival and longitudinal data, statistical methods for epidemiology, and bioinformatics.

Download or read book Efficient and Inefficient Estimation in Semiparametric Models written by M. J. van der Laan and published by . This book was released on 1995 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Contributions to Semiparametric Inference and Its Applications written by Seong Ho Lee and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation focuses on developing statistical methods for semiparametric inference and its applications. Semiparametric theory provides statistical tools that are flexible and robust to model misspecification. Utilizing the theory, this work proposes robust estimation approaches that are applicable to several scenarios with mild conditions, and establishes their asymptotic properties for inference. Chapter 1 provides a brief review of the literature related to this work. It first introduces the concept of semiparametric models and the efficiency bound. It further discusses two nonparametric techniques employed in the following chapters, kernel regression and B-spline approximation. The chapter then addresses the concept of dataset shift. In Chapter 2, novel estimators of causal effects for categorical and continuous treatments are proposed by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent for causal contrasts and asymptotically normal, when either the model explaining the treatment assignment is correctly specified, or the correct set of bases for the outcome models has been chosen and the assignment model is sufficiently rich. Asymptotic results are complemented with simulations illustrating the finite sample properties. A data analysis suggests a nonlinear effect of BMI on self-reported health decline among the elderly. In Chapter 3, we consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze non-labor income data and discover a new interesting predictor. In Chapter 4, we propose a procedure to select the best training subsample for a classification model. Identifying patient's disease status from electronic health records (EHR) is a frequently encountered task in EHR related research. However, assessing patient's phenotype is costly and labor intensive, hence a proper selection of EHR as a training set is desired. We propose a procedure to tailor the training subsample for a classification model minimizing its mean squared error (MSE). We provide theoretical justification on its optimality in terms of MSE. The performance gain from our method is illustrated through simulation and a real data example, and is found often satisfactory under criteria beyond mean squared error. In Chapter 5, we study label shift assumption and propose robust estimators for quantities of interest. In studies ranging from clinical medicine to policy research, the quantity of interest is often sought for a population from which only partial data is available, based on complete data from a related but different population. In this work, we consider this setting under the so-called label shift assumption. We propose an estimation procedure that only needs standard nonparametric techniques to approximate a conditional expectation, while by no means needs estimates for other model components. We develop the large sample theory for the proposed estimator, and examine its finite-sample performance through simulation studies, as well as an application to the MIMIC-III database.

Download or read book Nonparametric and Semiparametric Regression with Missing Data written by Lu Wang and published by . This book was released on 2008 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we consider nonparametric and semiparametric regression for both independent and longitudinal data with missing at random (MAR). The thesis consists of three chapters. In chapter 1, we focus on nonparametric regression of a scalar outcome on a covariate when the outcome is MAR. We show that the usual nonparametric kernel regression estimation based only on complete cases is generally inconsistent. We propose inverse probability weighted (IPW) kernel estimating equations (KEEs) and a class of augmented IPW (AIPW) KEEs. Both approaches do not require specification of a parametric model for the error distribution. We show that the IPW kernel estimator is consistent when the probability that a sampling unit is observed, i.e., the selection probability, is known by design or is estimated using a correctly specified model. We further show that the AIPW kernel estimator is double-robust in the sense that it is consistent if either the model for the selection probability or the model for the conditional mean of the outcome given covariates and auxiliary variables is correctly specified, not necessarily both. We argue that adequate augmentation terms in the AIPW KEEs help increase the efficiency of the estimator. We study the asymptotic properties of the proposed IPW and AIPW kernel estimators, perform simulations to evaluate their finite sample performance, and apply to the analysis of the AIDS Costs and Services Utilization Survey data.

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 Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 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 Nonparametric Estimation of Conditional Expectation with Auxiliary Information and Dimension Reduction written by Bingying Xie and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric estimation of the conditional expectation E(Y|U)) of an outcome Y given a covariate vector U is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable Z in the training dataset used to construct estimators. But Z is not available for future prediction or analysis in personalized medicine. For example, in the training dataset the outcome is longitudinal, but only the end point Y is concerned in the future prediction or analysis. The longitudinal outcomes other than the end point is then the variable Z that is observed and related with both Y and U. Previous work on how to make use of Z in the estimation of E(Y|U)) mainly focused on using Z in the construction of a linear function of U to reduce covariate dimension for better estimation. Using E(Y|U)) = E{E(Y|U), Z)|U}, we propose a two-step estimation of inner and outer expectations, respectively, with sufficient dimension reduction for kernel estimation in both steps. The information Z is utilized not only in dimension reduction, but also directly in the estimation. Because of the existence of different ways for dimension reduction, we construct two estimators that may improve the estimator without using Z. The improvements are shown in the convergence rate of estimators as the sample size increases to infinity as well as in the finite sample simulation performance. A real data analysis about the selection of mammography intervention is presented for illustration.

Download or read book Essays on Treatment Effect Estimation and Treatment Choice Learning written by Liqiang Shi and published by . This book was released on 2022 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three chapters that study treatment effect estimation and treatment choice learning under the potential outcome framework (Neyman, 1923; Rubin, 1974). The first two chapters study how to efficiently combine an experimental sample with an auxiliary observational sample when estimating treatment effects. In chapter 1, I derive a new semiparametric efficiency bound under the two-sample setup for estimating ATE and other functions of the average potential outcomes. The efficiency bound for estimating ATE with an experimental sample alone is derived in Hahn (1998) and has since become an important reference point for studies that aim at improving the ATE estimation. This chapter answers how an auxiliary sample containing only observable characteristics (covariates, or features) can lower this efficiency bound. The newly obtained bound has an intuitive expression and shows that the (maximum possible) amount of variance reduction depends positively on two factors: 1) the size of the auxiliary sample, and 2) how well the covariates predict the individual treatment effect. The latter naturally motivates having high dimensional covariates and the adoption of modern machine learning methods to avoid over-fitting. In chapter 2, under the same setup, I propose a two-stage machine learning (ML) imputation estimator that achieves the efficiency bound derived in chapter 1, so that no other regular estimators for ATE can have lower asymptotic variance in the same setting. This estimator involves two steps. In the first step, conditional average potential outcome functions are estimated nonparametrically via ML, which are then used to impute the unobserved potential outcomes for every unit in both samples. In the second step, the imputed potential outcomes are aggregated together in a robust way to produce the final estimate. Adopting the cross-fitting technique proposed in Chernozhukov et al. (2018), our two-step estimator can use a wide range of supervised ML tools in its first step, while maintaining valid inference to construct confidence intervals and perform hypothesis tests. In fact, any method that estimates the relevant conditional mean functions consistently in square norm, with no rate requirement, will lead to efficiency through the proposed two-step procedure. I also show that cross-fitting is not necessary when the first step is implemented via LASSO or post-LASSO. Furthermore, our estimator is robust in the sense that it remains consistent and root n normal (no longer efficient) even if the first step estimators are inconsistent. Chapter 3 (coauthored with Kirill Ponomarev) studies model selection in treatment choice learning. When treatment effects are heterogeneous, a decision maker, given either experiment or quasi-experiment data, can attempt to find a policy function that maps observable characteristics to treatment choices, aiming at maximizing utilitarian welfare. When doing so, one often has to pick a constrained class of functions as candidates for the policy function. The choice of this function class poses a model selection problem. Following Mbakop and Tabord-Meehan (2021) we propose a policy learning algorithm that incorporates data-driven model selection. Our method also leverages doubly robust estimation (Athey and Wager, 2021) so that it could retain the optimal root n rate in expected regret in general setups including quasi-experiments where propensity scores are unknown. We also refined some related results in the literature and derived a new finite sample lower bound on expected regret to show that the root n rate is indeed optimal.

Download or read book The New Palgrave Dictionary of Economics written by and published by Springer. This book was released on 2016-05-18 with total page 7493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product.

Download or read book Semiparametric Estimation and Efficiency Results for Some Sample Models written by Songnian Chen and published by . This book was released on 1994 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2008 with total page 1788 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Semiparametric Estimators for Nonlinear Regressions and Models Under Sample Selection Bias written by Mi Jeong Kim and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the consistency, robustness and efficiency of parameter estimation in different but related models via semiparametric approach. First, we revisit the second-order least squares estimator proposed in Wang and Leblanc (2008) and show that the estimator reaches the semiparametric efficiency. We further extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Second, we study a class of semiparametric skewed distributions arising when the sample selection process causes sampling bias for the observations. We begin by assuming the anti-symmetric property to the skewing function. Taking into account the symmetric nature of the population distribution, we propose consistent estimators for the center of the symmetric population. These estimators are robust to model misspecification and reach the minimum possible estimation variance. Next, we extend the model to permit a more flexible skewing structure. Without assuming a particular form of the skewing function, we propose both consistent and efficient estimators for the center of the symmetric population using a semiparametric method. We also analyze the asymptotic properties and derive the corresponding inference procedures. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimators.

Download or read book A Note on Semiparametric Estimation of Finite Mixtures of Discrete Choice Models with Application to Game Theoretic Models written by Patrick Bajari and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We view a game abstractly as a semiparametric mixture distribution and study the semiparametric efficiency bound of this model. Our results suggest that a key issue for inference is the number of equilibria compared to the number of outcomes. If the number of equilibria is sufficiently large compared to the number of outcomes, root-n consistent estimation of the model will not be possible. We also provide a simple estimator in the case when the efficiency bound is strictly above zero.