Nonparametric Regression With The Scale Depending On Auxiliary Covariates And Missing Data
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Nonparametric Regression With The Scale Depending On Auxiliary Covariates And Missing Data
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Author : Tian Jiang
language : en
Publisher:
Release Date : 2022
Nonparametric Regression With The Scale Depending On Auxiliary Covariates And Missing Data written by Tian Jiang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Heteroscedasticity categories.
Nonparametric curve estimation is a powerful statistical methodology which allows estimation of curves with no assumption about their shape. It provides useful insight into the nature of data and may guide further inference for specific parametric models. Considered statistical problem is a nonparametric heteroscedastic regression with auxiliary covariates and missing data. In this regression a univariate component is of the primary interest while the scale function is allowed to be dependent on both the predictor and auxiliary covariates. Missing mechanism is the missing at random (MAR), and two settings with missing responses or missing predictors are considered. The assumed MAR means that the probability of missing may depend on observed variables but not on missing variables. Developed asymptotic theory shows how the heteroscedasticity and MAR mechanism affect the constant of minimax convergence under the mean integrated squared error criterion. Further, it is shown that a procedure ignoring the scale function is not efficient and does not attain a sharp constant in the minimax lower bound. Models of missing responses and predictors are considered separately because their theory and methodology are different. For the case of missing responses, a sharp minimax and data-driven procedure is developed which is based on estimation of an unknown nuisance scale function. The estimator adapts to the MAR response mechanism and unknown smoothness of an underlying regression function. Further, efficiency is still preserved for a more general additive model with auxiliary covariates. A model with MAR predictors is dramatically more involved, and here classic regression estimators are no longer even consistent. For a model with MAR predictors a novel data-driven estimator is suggested which takes into account a scale function. This estimator is adaptive and matches performance of an oracle that knows all underlying nuisance functions. The asymptotic theory is extended to the case of a general additive model as well. The theory and methodology are tested using Monte Carlo simulation studies and real examples. The results favor the proposed methodology and support practical feasibility of the proposed methods for heteroscedastic regressions with missing data.
Missing And Modified Data In Nonparametric Estimation
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Author : Sam Efromovich
language : en
Publisher: CRC Press
Release Date : 2018-03-12
Missing And Modified Data In Nonparametric Estimation written by Sam Efromovich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-12 with Mathematics categories.
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
Strategies To Approximate Random Sampling And Assignment
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Author : Patrick Dattalo
language : en
Publisher: Oxford University Press
Release Date : 2009-10-29
Strategies To Approximate Random Sampling And Assignment written by Patrick Dattalo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-29 with Social Science categories.
Random sampling and random assignment are considered by many researchers to be the definitive methodological procedures for maximizing external and internal validity. However, there is a daunting list of legal, ethical, and practical barriers to implementing random sampling and random assignment. While there are no easy ways to overcome these barriers, social workers should seek and utilize strategies that minimize sampling and assignment bias. These methodological and statistical strategies form the book's core. In step-by-step chapters liberally illustrated with examples using a variety of software packages, Dattalo guides readers in selecting and implementing an appropriate strategy. Readers will gain confidence in using such techniques as exemplar sampling, sequential sampling, randomization tests, multiple imputation, mean-score logistic regression, partial randomization, constructed comparison groups, instrumental variables methods, and propensity scores. Each approach will be cataloged in such a way as to highlight its underlying assumptions, implementation strategies, and strengths and weaknesses. Screen shots, annotated resources, and a companion website make this a valuable tool for students, teachers, and researchers seeking a single source that provides a diverse set of tools that will maximize a study's validity when random sampling and random assignment are neither possible nor practical.
Logistic Regression With Missing Values In The Covariates
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Author : Werner Vach
language : en
Publisher:
Release Date : 1994
Logistic Regression With Missing Values In The Covariates written by Werner Vach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Estimation theory categories.
Review Of Recreational Fisheries Survey Methods
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 2006-08-13
Review Of Recreational Fisheries Survey Methods written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-13 with Technology & Engineering categories.
Recreational fishing in the United States is an important social and economic component of many marine fisheries, with an estimated 14 million anglers making almost 82 million fishing trips in 2004. Although each individual angler typically harvests a small number of fish, collectively these sport fisheries can take a significant fraction of the yearly catch-in some cases more than commercial fisheries. For example, in 1999, recreational fishing accounted for 94% of the total catch of spotted sea trout, 76% of striped bass and sheephead, and 60 percent of king mackerel. It is important that systems used to monitor fishing catch are adequate for timely management of recreational fisheries. However, the large number of anglers and access points makes monitoring recreational fishing much more difficult than monitoring commercial fishing. This report reviews the types of survey methods used to estimate catch in recreational fisheries, including state/federal cooperative programs. The report finds that both telephone survey and onsite access components of the current monitoring systems have serious flaws in design or implementation. There are also several areas of miscommunication and mismatched criteria among designers of surveys, data collectors, and recreational fisheries. The report recommends that a comprehensive, universal sampling frame with national coverage should be established, and that improvements should be made in statistical analysis of the data collected and in the ways the data are communicated. A permanent and independent research group should be established and funded to evaluate the statistical design and adequacy of recreational fishery surveys and to guide necessary modifications or new initiatives.
Journal Of The American Statistical Association
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Author :
language : en
Publisher:
Release Date : 2008
Journal Of The American Statistical Association written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Electronic journals categories.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2005
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Dissertations, Academic categories.
Bayesian Nonparametric Data Analysis
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Author : Peter Müller
language : en
Publisher: Springer
Release Date : 2015-06-17
Bayesian Nonparametric Data Analysis written by Peter Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-17 with Mathematics categories.
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.
Mixed Effects Models For Complex Data
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Author : Lang Wu
language : en
Publisher: CRC Press
Release Date : 2009-11-11
Mixed Effects Models For Complex Data written by Lang Wu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-11 with Mathematics categories.
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.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.