Empirical Likelihood for Random Sets

Empirical Likelihood for Random Sets
Author:
Publisher:
Total Pages:
Release: 2017
Genre:
ISBN:

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Abstract: In many statistical applications, the observed data take the form of sets rather than points. Examples include bracket data in survey analysis, tumor growth and rock grain images in morphology analysis, and noisy measurements on the support function of a convex set in medical imaging and robotic vision. Additionally, in studies of treatment effects, researchers often wish to conduct inference on nonparametric bounds for the effects which can be expressed by means of random sets. This article develops the concept of nonparametric likelihood for random sets and its mean, known as the Aumann expectation, and proposes general inference methods by adapting the theory of empirical likelihood. Several examples, such as regression with bracket income data, Boolean models for tumor growth, bound analysis on treatment effects, and image analysis via support functions, illustrate the usefulness of the proposed methods. Supplementary materials for this article are available online.

Empirical Likelihood

Empirical Likelihood
Author: Art B. Owen
Publisher: CRC Press
Total Pages: 322
Release: 2001-05-18
Genre: Mathematics
ISBN: 1420036157

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Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al

Random Sets in Econometrics

Random Sets in Econometrics
Author: Ilya Molchanov
Publisher: Cambridge University Press
Total Pages: 199
Release: 2018-04-05
Genre: Business & Economics
ISBN: 1108651356

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Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.

Empirical Likelihood Method in Survival Analysis

Empirical Likelihood Method in Survival Analysis
Author: Mai Zhou
Publisher: CRC Press
Total Pages: 221
Release: 2015-06-17
Genre: Mathematics
ISBN: 1466554932

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Empirical Likelihood Method in Survival Analysis explains how to use the empirical likelihood method for right censored survival data. The author uses R for calculating empirical likelihood and includes many worked out examples with the associated R code. The datasets and code are available for download on his website and CRAN. The book focuses on all the standard survival analysis topics treated with empirical likelihood, including hazard functions, cumulative distribution functions, analysis of the Cox model, and computation of empirical likelihood for censored data. It also covers semi-parametric accelerated failure time models, the optimality of confidence regions derived from empirical likelihood or plug-in empirical likelihood ratio tests, and several empirical likelihood confidence band results. While survival analysis is a classic area of statistical study, the empirical likelihood methodology has only recently been developed. Until now, just one book was available on empirical likelihood and most statistical software did not include empirical likelihood procedures. Addressing this shortfall, this book provides the functions to calculate the empirical likelihood ratio in survival analysis as well as functions related to the empirical likelihood analysis of the Cox regression model and other hazard regression models.

Random Sets in Econometrics

Random Sets in Econometrics
Author: Ilya Molchanov
Publisher: Cambridge University Press
Total Pages: 199
Release: 2018-04-12
Genre: Business & Economics
ISBN: 1107121205

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This is the first full-length study of how the theory of random sets can be applied in econometrics.

Sample Surveys: Inference and Analysis

Sample Surveys: Inference and Analysis
Author:
Publisher: Morgan Kaufmann
Total Pages: 667
Release: 2009-09-02
Genre: Mathematics
ISBN: 0080963544

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Handbook of Statistics_29B contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications. Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects. Comprehensive account of recent developments in sample survey theory and practice Covers a wide variety of diverse applications Comprehensive bibliography

Empirical Likelihood Inference for Random Coefficient INAR(P) Process

Empirical Likelihood Inference for Random Coefficient INAR(P) Process
Author: Haixiang Zhang
Publisher:
Total Pages: 0
Release: 2011
Genre:
ISBN:

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In this article, we study the empirical likelihood (EL) method for the pth-order random coefficient integer-valued autoregressive process. In particular, the limiting distribution of the log EL ratio statistic is established and the confidence regions for the parameter of interest are derived. Also a simulation study is conducted for the evaluation of the developed approach.

Theory of Random Sets

Theory of Random Sets
Author: Ilya Molchanov
Publisher: Springer Science & Business Media
Total Pages: 501
Release: 2005-11-28
Genre: Mathematics
ISBN: 1846281504

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This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine

An Introduction to Random Sets

An Introduction to Random Sets
Author: Hung T. Nguyen
Publisher: CRC Press
Total Pages: 268
Release: 2006-03-27
Genre: Mathematics
ISBN: 1420010611

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The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i