Author: Alex Catane BajamondePublisher:
ISBN:
Category :
Languages : en
Pages : 260
Book Description
On Efficient and Robust Estimation in Semiparametric Linear Regression Models with Missing Data
Author: Alex Catane BajamondePublisher:
ISBN:
Category :
Languages : en
Pages : 260
Book Description
Semiparametric Theory and Missing Data
Author: Anastasios TsiatisPublisher: Springer Science & Business Media
ISBN: 0387373454
Category : Mathematics
Languages : en
Pages : 392
Book Description
This book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.
Robust Estimation with Discrete Explanatory Variables
Author: Pavel CizekPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
The least squares estimator is probably the most frequently used estimation method in regression analysis. Unfortunately, it is also quite sensitive to data contamination and model misspecification. Although there are several robust estimators designed for parametric regression models that can be used in place of least squares, these robust estimators cannot be easily applied to models containing binary and categorical explanatory variables. Therefore, I design a robust estimator that can be used for any linear regression model no matter what kind of explanatory variables the model contains. Additionally, I propose an adaptive procedure that maximizes the efficiency of the proposed estimator for a given data set while preserving its robustness.
Robust Estimation of Semiparametric Regression Models
Author: Martin R. YoungPublisher:
ISBN:
Category : Least absolute deviations (Statistics)
Languages : en
Pages : 31
Book Description
Robust Estimation in Semiparametric Models
Author: Zaiqian ShenSelected Works of Peter J. Bickel
Author: Jianqing FanPublisher: Springer Science & Business Media
ISBN: 1461455448
Category : Mathematics
Languages : en
Pages : 626
Book Description
This volume presents selections of Peter J. Bickel’s major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peter’s amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peter’s life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.
Statistical Analysis of Missing Not at Random Problems with a Nonparametric Regression Model and Semiparametric Missingness Mechanism
Author: Samidha Sudhakar ShettyPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Missing data is common in data sets in every field of science. In the past few decades, there has been interest in understanding the underlying pattern of missingness, formally known as the missingness mechanism. There are three types of missingness mechanisms: Missing Completely at Random (MCAR), Missing at Random (MAR) and Missing Not at Random (MNAR). These can also be classified into two main categories: Ignorable (MCAR and MAR) and Nonignorable (MNAR). Most likelihood or imputation-based methods developed assume the ignorable condition, which is the more well studied condition. We discuss the nonignorable condition which is less well studied and also the hardest to deal with. This dissertation consists of three chapters that address the issue of estimation under the nonignorable missing data setting. In the first chapter, we propose a robust estimator of a parameter or a summary quantity of the model parameters in the context where outcome is subject to nonignorable missingness. These estimators are robust to misspecification of the dependence on covariates. The robustness of the estimators are nonstandard and are established rigorously through theoretical derivations, and are supported by simulations and a data application. In the second chapter, we attempt the efficient estimation of a function of the response under nonignorable missingness. We briefly discuss efficiency and robustness of estimators under the ignorable missingness assumption which is well established. However, efficiency under the nonignorable setting requires more investigation. We derive the efficient score for a function of the response but it turns out to be very complex and infeasible. Therefore, we recommend trading efficiency in favor of feasibility and using an inefficient but consistent estimator. In the final chapter, we propose an efficient estimator for the parameter involved in the missingness propensity. We first estimate the dependence of the missingness on the covariates. We incorporate the above estimator to construct an efficient estimator for the parameter of interest. We study the theoretical properties of this estimator and also put forward an alternative estimator for the mean of the response.
Semiparametric Odds Ratio Model and Its Applications
Author: Hua Yun ChenPublisher: CRC Press
ISBN: 1351049747
Category : Mathematics
Languages : en
Pages : 296
Book Description
Beginning with familiar models and moving onto advanced semiparametric modelling tools Semiparametric Odds Ratio Model and its Applications introduces readers to a new range of flexible statistical models and provides guidance on their application using real data examples. This books range of real-world examples and exploration of common statistical problems makes it an invaluable reference for research professionals and graduate students of biostatistics, statistics, and other quantitative fields. Key Features: Introduces flexible statistical models that have yet to systematically introduced in course materials. Discusses applications of the proposed modelling framework in several important statistical problems, ranging from biased sampling designs and missing data, graphical models, survival analysis, Gibbs sampler and model compatibility, and density estimation. Includes real data examples to demonstrate the use of the proposed models, and estimation and inference tools.
Robust Statistics, Data Analysis, and Computer Intensive Methods
Author: Helmut RiederPublisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 454
Book Description
This book gathers together a wide range of contributions on modern techniques which are becoming widely used in statistics. These methods include the bootstrap, nonparametric density estimation, robust regression, and projections and sections.
Author: Pavel Čížek