Partial identification of probability distributions.
type: Item
instance of: scholarly article
title: Partial identification of probability distributions.
zbMATH Open document ID: 1047.62001
author: Charles F. Manski
published in: Springer Series in Statistics
publication date: 2003-06-22T00:00:00Z
review text: This book is an excellent and rigorous presentation of the state of research in the area of partial identification of populations and credible inference, in which the author has made many important contributions. The main theme of the book stems from the author's research in nonparametric regression analysis using data generated by random sampling processes with partial observability of outcomes if nothing is known about the missingness mechanisms. It reveals why there is much scope for statistical inference, mainly nonparametric, using data and assumptions in partially identifying the parameters of a population and how such inference can be made. The material is organized in ten chapters. Chapter 1 is devoted to the study of identification using empirical evidence and to the description of the identification regions of specific population parameters. The foundation of random sampling is extended to cases where the data generating mechanisms are multiple random sampling processes, each with only partially observable outcomes. Further, the problem of sampling with missing outcomes is presented as a special case of the problem of interval measurements of outcomes. Chapter 2 refers to various types of assumptions on the distributions of populations under study that employ instrumental variables as an aid in identifying their forms. Starting with the common assumptions that data are missing at random and that outcomes are statistically independent, the focus turns on the identification of expectations of real-valued functions of the outcomes under the weaker assumptions of mean independence of outcomes and of means missing at random. These assumptions are further weakened to distributional assumptions implying various types of monotonicity in the form of missingness of the outcomes (means missing monotonically) or replacing statistical independence of outcomes with some form of monotonicity in their means. The analysis readily extends to inference on conditional outcome…
reviewed by: Evdokia Xekalaki
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62E99
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62P20
zbMATH DE Number: 1932063
zbMATH Keywords: partial identification
zbMATH Keywords: prediction with missing data
zbMATH Keywords: instrumental variables
zbMATH Keywords: response-based sampling
zbMATH Keywords: treatment response
zbMATH Keywords: monotonicity
zbMATH Keywords: mean independence
zbMATH Keywords: mean monotonicity
zbMATH Keywords: contaminated outcomes
zbMATH Keywords: mixture models
MaRDI profile type: Publication
full work available at URL: b97478
OpenAlex ID: W1544362532
DOI: 10.1007/B97478
description: scientific article; zbMATH DE number 1932063