Information Bounds and Nonparametric Maximum Likelihood Estimation

Information Bounds and Nonparametric Maximum Likelihood Estimation
Title Information Bounds and Nonparametric Maximum Likelihood Estimation PDF eBook
Author P. Groeneboom
Publisher Birkhäuser
Pages 129
Release 2012-12-06
Genre Mathematics
ISBN 3034886217

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This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem.

Information Bounds and Nonparametric Maximum Likelihood Estimation

Information Bounds and Nonparametric Maximum Likelihood Estimation
Title Information Bounds and Nonparametric Maximum Likelihood Estimation PDF eBook
Author P. Groeneboom
Publisher Birkhauser
Pages 126
Release 1992
Genre Mathematics
ISBN 9780817627942

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Non-parametric Maximum Likelihood Estimation

Non-parametric Maximum Likelihood Estimation
Title Non-parametric Maximum Likelihood Estimation PDF eBook
Author G. B. Crawford
Publisher
Pages 21
Release 1963
Genre
ISBN

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Given that a distribution function is a member of a subclass of absolutely continuous measures, the problem of nonparametric estimation is considered, with the method of maximum likelihood, of the underlying density function of a given sample of independent identically distributed random variables. Sufficient conditions on the space of probability densities and its topology are given for the consistency of such an estimate. (Author).

Maximum Likelihood Estimation: a Practical Theorem on Consistency of the Nonparametric Maximum Likelihood Estimates with Applications

Maximum Likelihood Estimation: a Practical Theorem on Consistency of the Nonparametric Maximum Likelihood Estimates with Applications
Title Maximum Likelihood Estimation: a Practical Theorem on Consistency of the Nonparametric Maximum Likelihood Estimates with Applications PDF eBook
Author
Publisher
Pages 21
Release 1967
Genre
ISBN

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Sufficient conditions for consistency of a nonparametric maximum likelihood estimate are given which are applicable to those problems where a class of distribution functions is specified only in terms of its graphs. Consistency is proven and applications are given. (Author).

Nonparametric Maximum Likelihood Estimation of the Cumulative Distribution Function with Multivariate Interval Censored Data

Nonparametric Maximum Likelihood Estimation of the Cumulative Distribution Function with Multivariate Interval Censored Data
Title Nonparametric Maximum Likelihood Estimation of the Cumulative Distribution Function with Multivariate Interval Censored Data PDF eBook
Author Xuecheng Liu
Publisher
Pages 172
Release 2002
Genre
ISBN

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"This thesis addresses nonparametric maximal likelihood (NPML) estimation of the cumulative distribution function (CDF) given multivariate interval censored data (MILD). The methodology consists in applying graph theory to the intersection graph of censored data. The maximal cliques of this graph and their real representations contain all the information needed to find NPML estimates (NPMLE). In this thesis, a new algorithm to determine the maximal cliques of an MICD set is introduced. The concepts of diameter and semi-diameter of the polytope formed by all NPMLEs are introduced and simulation to investigate the properties of the non-uniqueness polytope of the CDF NPMLEs for bivariate censored data is described. Also, an a priori bounding technique for the total mass attributed to a set of maximal cliques by a self-consistent estimate of the CDF (including the NPMLE) is presented." --

Interval-Censored Time-to-Event Data

Interval-Censored Time-to-Event Data
Title Interval-Censored Time-to-Event Data PDF eBook
Author Ding-Geng (Din) Chen
Publisher CRC Press
Pages 426
Release 2012-07-19
Genre Mathematics
ISBN 1466504285

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Interval-Censored Time-to-Event Data: Methods and Applications collects the most recent techniques, models, and computational tools for interval-censored time-to-event data. Top biostatisticians from academia, biopharmaceutical industries, and government agencies discuss how these advances are impacting clinical trials and biomedical research.Divid

Emerging Topics in Modeling Interval-Censored Survival Data

Emerging Topics in Modeling Interval-Censored Survival Data
Title Emerging Topics in Modeling Interval-Censored Survival Data PDF eBook
Author Jianguo Sun
Publisher Springer Nature
Pages 322
Release 2022-11-29
Genre Mathematics
ISBN 3031123662

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This book primarily aims to discuss emerging topics in statistical methods and to booster research, education, and training to advance statistical modeling on interval-censored survival data. Commonly collected from public health and biomedical research, among other sources, interval-censored survival data can easily be mistaken for typical right-censored survival data, which can result in erroneous statistical inference due to the complexity of this type of data. The book invites a group of internationally leading researchers to systematically discuss and explore the historical development of the associated methods and their computational implementations, as well as emerging topics related to interval-censored data. It covers a variety of topics, including univariate interval-censored data, multivariate interval-censored data, clustered interval-censored data, competing risk interval-censored data, data with interval-censored covariates, interval-censored data from electric medical records, and misclassified interval-censored data. Researchers, students, and practitioners can directly make use of the state-of-the-art methods covered in the book to tackle their problems in research, education, training and consultation.