Efromovich S. Missing and Modified Data in Nonparametric Estimation: With R Examples

New York: Chapman and Hall/CRC, 2018. — 464 p. — ISBN: 978-1-138-05488-2This 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.Density Estimation for Missing and Modified Data
Nonparametric Regression with Missing Data
Notions and Notations
Software
Inside the Book
Estimation for Directly Observed Data
Series Approximation
Density Estimation for Complete Data
Nonparametric Regression
Bernoulli Regression
Multivariate Series Estimation
Confidence Bands
Estimation for Basic Models of Modified Data
Density Estimation for Biased Data
Regression with Biased Responses
Regression with Biased Predictors and Responses
Ordered Grouped Responses
Mixture
Nuisance Functions
Bernoulli Regression with Unavailable Failures
Nondestructive Missing
Density Estimation with MCAR Data
Nonparametric Regression with MAR Responses
Nonparametric Regression with MAR Predictors
Conditional Density Estimation
Poisson Regression with MAR Data
Estimation of the Scale Function with MAR Responses
Bivariate Regression with MAR Responses
Additive Regression with MAR Responses
Destructive Missing
Density Estimation When the Availability Likelihood is Known
Density Estimation with an Extra Sample
Density Estimation with Auxiliary Variable
Regression with MNAR Responses
Regression with MNAR Predictors
Missing Cases in Regression
Survival Analysis
Hazard Rate Estimation for Direct Observations
Censored Data and Hazard Rate Estimation
Truncated Data and Hazard Rate Estimation
LTRC Data and Hazard Rate Estimation
Estimation of Distributions for RC Data
Estimation of Distributions for LT Data
Estimation of Distributions for LTRC Data
Nonparametric Regression with RC Responses
Nonparametric Regression with RC Predictors
Missing Data in Survival Analysis
MAR Indicator of Censoring in Estimation of Distribution
MNAR Indicator of Censoring in Estimation of Distribution
MAR Censored Responses
Censored Responses and MAR Predictors
Censored Predictors and MAR Responses
Truncated Predictors and MAR Responses
LTRC Predictors and MAR Responses
Time Series
Discrete-Time Series
Density and Its Estimation
Bernoulli Missing
Amplitude-Modulated Missing
Censored Time Series
Probability Density Estimation
Nonparametric Autoregression
Dependent Observations
Nonparametric Regression
Stochastic Process
Nonstationary Time Series With Missing Data
Decomposition of Amplitude-Modulated Time Series
Nonstationary Amplitude-Modulation
Nonstationary Autocovariance and Spectral Density
The Simpson Paradox
Sequential Design
Ill-Posed Modifications
Measurement Errors in Density Estimation
Density Deconvolution with Missing Data
Density Deconvolution for Censored Data
Current Status Censoring
Regression with Measurement Errors in Predictors
MEP Regression with Missing Responses
Estimation of Derivative