Likelihood

Author: A. W. F. Edwards

Publisher: CUP Archive

ISBN: 9780521318716

Category: Mathematics

Page: 235

View: 4271

Dr Edwards' stimulating and provocative book advances the thesis that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but rather likelihood - the concept introduced by Fisher as a measure of relative support amongst different hypotheses. Starting from the simplest considerations and assuming no more than a modest acquaintance with probability theory, the author sets out to reconstruct nothing less than a consistent theory of statistical inference in science.
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Likelihood-basierte Entscheidungstheorie unter Unsicherheit. Das Minimax-Prinzip und das Bayes-Prinzip

Author: Claudio Salvati

Publisher: GRIN Verlag

ISBN: 3668449147

Category: Mathematics

Page: 23

View: 8701

Studienarbeit aus dem Jahr 2017 im Fachbereich Statistik, Note: 2,00, Ludwig-Maximilians-Universität München (Institut für Statistik), Veranstaltung: Fortgeschrittene Themen der Entscheidungstheorie, Sprache: Deutsch, Abstract: Die vorliegende Arbeit wird zunächst die Grundlagen der Entscheidungstheorie skizzieren, zwei bekannte Verfahren - das Minimax-Prinzip und das Bayes-Prinzip - vorstellen und anhand eines praktischen Beispiels aus der Vorlesung die Vorgehensweise veranschaulichen. Der Fokus liegt allerdings auf einem der Likelihood-Funktion zugrunde liegenden Entscheidungsverfahren: Im Hauptteil werden zunächst die der Likelihood zu Grunde liegende Idee und die Annahmen sowie Eigenschaften der Likelihood-Funktion erläutert und danach Entscheidungsverfahren und ihre Umsetzung eingeführt, die auf ihr basieren.
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Parametrische Statistik

Verteilungen, maximum likelihood und GLM in R

Author: Carsten F. Dormann

Publisher: Springer-Verlag

ISBN: 3662546841

Category: Medical

Page: 363

View: 452

Beispielreich baut dieses Buch Schritt für Schritt die statistischen Grundlagen moderner Datenanalysen auf. Im Gegensatz zu anderen einführenden Werken legt dieses Buch großen Wert auf einen umfassend gespannten Bogen, einen roten Faden, der alle Methoden zusammenführt. Dabei werden klassische statistische Methoden (etwa t-Test oder multiple Regression) als Spezialfall des Generalisierten Linearen Modells entwickelt. Entsprechend legt das Buch zunächst eine Grundlage in beschreibender Statistik, Verteilungen und maximum likelihood, aus der dann alle anderen Verfahren abgeleitet werden (ANOVA, multiple Regression). Jeder Schritt ist auf zwei Kapitel verteilt: Im ungradzahligen Kapitel wird anhand von vielen Beispielen und Abbildungen die Idee der statistischen Herangehensweise erläutert. Im sich daran anschließenden gradzahligen Kapitel wird die Umsetzung in der freien Statistiksoftware R gezeigt. Ein Kapitel zur Wissenschafts- und Forschungstheorie und eines zum Design von Experimenten und Stichprobeverfahren komplettiert dieses einleitende Werk. Das Buch legt großen Wert auf Verständlichkeit und Umsetzung. Mathematische Herleitungen treten demgegenüber stark in den Hintergrund. Jedes Kapitel enthält explizit ausgewiesene Lerninhalte, die durch Übungen zu jedem R-Kapitel geprüft werden können. Ein ausführliches Schlagwortverzeichnis inklusive der R-Funktionen macht das Buch auch als Nachschlagewerk nutzbar. Die zweite Auflage wurde ergänzt um Schätzung mittels der Momentenmethode, Residuendiagnostik für nicht-normalverteilte Daten und die erschöpfende Modellsuche.
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Maximum Likelihood Estimation

Logic and Practice

Author: Scott R. Eliason

Publisher: SAGE

ISBN: 9780803941076

Category: Mathematics

Page: 87

View: 7397

In this volume the underlying logic and practice of maximum likelihood (ML) estimation is made clear by providing a general modeling framework that utilizes the tools of ML methods. This framework offers readers a flexible modeling strategy since it accommodates cases from the simplest linear models to the most complex nonlinear models that link a system of endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, Eliason discusses: what properties are desirable in an estimator; basic techniques for finding ML solutions; the general form of the covariance matrix for ML estimates; the sampling distribution of ML estimators; the application of ML in the normal distribution as well as in other useful distributions; and some helpful illustrations of likelihoods.
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The Likelihood Principle

Author: James O. Berger,Robert L. Wolpert

Publisher: IMS

ISBN: 9780940600133

Category: Mathematics

Page: 208

View: 1870

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Maximum Likelihood Estimation with Stata, Third Edition

Author: William Gould,Jeffrey Pitblado,William Sribney

Publisher: Stata Press

ISBN: 1597180122

Category: Computers

Page: 290

View: 1068

Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.
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Maximum Penalized Likelihood Estimation

Volume II: Regression

Author: Paul P. Eggermont,Vincent N. LaRiccia

Publisher: Springer Science & Business Media

ISBN: 0387689028

Category: Mathematics

Page: 572

View: 830

Unique blend of asymptotic theory and small sample practice through simulation experiments and data analysis. Novel reproducing kernel Hilbert space methods for the analysis of smoothing splines and local polynomials. Leading to uniform error bounds and honest confidence bands for the mean function using smoothing splines Exhaustive exposition of algorithms, including the Kalman filter, for the computation of smoothing splines of arbitrary order.
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Empirical Bayes and Likelihood Inference

Author: S.E. Ahmed,N. Reid

Publisher: Springer Science & Business Media

ISBN: 1461301416

Category: Mathematics

Page: 235

View: 1389

Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.
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Quasi-Likelihood And Its Application

A General Approach to Optimal Parameter Estimation

Author: C. C. Heyde

Publisher: Springer Science & Business Media

ISBN: 9780387982250

Category: Mathematics

Page: 235

View: 6187

This is author-approved bcc: Quasi-likelihood is a very generally applicable estimating function based methodology for optimally estimating model parameters in systems subject to random effects. Only assumptions about means and covariances are required in contrast to the full distributional assumptions of ordinary likelihood based methodology. This monograph gives the first account in book form of all the essential features of the quasi-likelihood methodology,and stresses its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential princples rather than detailed proofs. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided. Readers are assumed to have a firm grounding in probability and statistics at the graduate level. Christopher Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He is a Fellow of the Australian Academy of Science and has been Foundation Dean of the School of Mathematical Sciences at the Australian National University and Foundation Director of the Key Centre for Statistical Sciences in Melbourne. He has served as President of the Bernoulli Society and Vice President of the International Statistical Institute and is Editor-in-Chief of the international probability journals "Journal of Applied Probability" and "Advances in Applied Probability". He has done considerable distinguished research in probability and statistics which has been honoured by the awards of the Pitman Medal (1988),Hannan Medal.
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Econometric Applications of Maximum Likelihood Methods

Author: J. S. Cramer

Publisher: CUP Archive

ISBN: 9780521378574

Category: Business & Economics

Page: 224

View: 5560

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own.
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Statistical Inference Based on the likelihood

Author: Adelchi Azzalini

Publisher: CRC Press

ISBN: 9780412606502

Category: Mathematics

Page: 352

View: 5488

The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.
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Information Bounds and Nonparametric Maximum Likelihood Estimation

Author: P. Groeneboom,J.A. Wellner

Publisher: Springer Science & Business Media

ISBN: 9783764327941

Category: Mathematics

Page: 128

View: 4463

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.
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Meta-analysis of Binary Data Using Profile Likelihood

Author: Dankmar Bohning,Sasivimol Rattanasiri,Ronny Kuhnert

Publisher: CRC Press

ISBN: 9781420011333

Category: Mathematics

Page: 208

View: 4758

Providing reliable information on an intervention effect, meta-analysis is a powerful statistical tool for analyzing and combining results from individual studies. Meta-Analysis of Binary Data Using Profile Likelihood focuses on the analysis and modeling of a meta-analysis with individually pooled data (MAIPD). It presents a unifying approach to modeling a treatment effect in a meta-analysis of clinical trials with binary outcomes. After illustrating the meta-analytic situation of an MAIPD with several examples, the authors introduce the profile likelihood model and extend it to cope with unobserved heterogeneity. They describe elements of log-linear modeling, ways for finding the profile maximum likelihood estimator, and alternative approaches to the profile likelihood method. The authors also discuss how to model covariate information and unobserved heterogeneity simultaneously and use the profile likelihood method to estimate odds ratios. The final chapters look at quantifying heterogeneity in an MAIPD and show how meta-analysis can be applied to the surveillance of scrapie. Containing new developments not available in the current literature, along with easy-to-follow inferences and algorithms, this book enables clinicians to efficiently analyze MAIPDs.
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Maximum-Likelihood- und Minimum-Distanz-Schätzer von Copula-Funktionen

Author: Paul Passek

Publisher: GRIN Verlag

ISBN: 366883704X

Category: Business & Economics

Page: 85

View: 639

Bachelorarbeit aus dem Jahr 2017 im Fachbereich BWL - Bank, Börse, Versicherung, Note: 1,3, Friedrich-Schiller-Universität Jena (Wirtschaftswissenschaftliche Fakultät), Sprache: Deutsch, Abstract: Im finanz- und versicherungswirtschaftlichem Umfeld spielt die Modellierung von Abhängigkeiten in diversen Anwendungsfällen eine zentrale Rolle. So kommt es beispielsweise in der Bankenpraxis dazu, Abhängigkeiten zwischen Risikofaktoren eines Portfolios zu modellieren. Bei der Ermittlung des Gesamtrisikoprofils spielt die Frage nach der geeigneten Zusammenführung der Risikoarten ebenso eine zentrale Rolle wie die Korrelationen zwischen den einzelnen Teilrisiken. Dabei soll das Konzept der Copula helfen die einzelnen Risiken verteilungsspezifisch zu simulieren und zu einer gemeinsamen Verteilung zu verknüpfen. Diese Arbeit, inhaltlich aus drei aufeinander aufbauenden Kapiteln bestehend, soll einführende und vertiefende Aspekte zur Copula-Theorie vermitteln. Dabei nimmt insbesondere die im vierten Hauptkapitel vorgestellte Simulationsstudie für Copula-Parameterschätzer eine zentrale Rolle in dieser Arbeit ein. Dementsprechend ist auch das Konzept so ausgerichtet, dass die Simulationsstudie sukzessive durch theoretische und beispielhafte Argumentationen vorbereitet und motiviert wird. Dabei wird zunächst im Kapitel 2 das Grundkonzept der Copula-Idee vorgestellt. Aufbauend auf der Konstruktion im bivariaten Modellkontext werden grafische und formale Eigenschaften dieses Konzepts vorgestellt ehe es anschließend auf den multivariaten Fall ausgeweitet wird. Die Quellenangaben werden jeweils im Text angegeben und es wird an entsprechenden Stellen auf weiterführende Aspekte oder tiefgründigere mathematische Aufarbeitungen hingewiesen. Nachdem die Grundlagen gelegt wurden, werden im Kapitel 3 verschiedene Copula-Arten vorgestellt und näher charakterisiert. Dabei soll bei der Erläuterung der Besonderheiten der einzelnen Copula-Klassen ein ausgewogener Mix zwischen mathematischer Formulierung und grafischer, beispielorientierter Argumentation herrschen. Darüber hinaus werden jeweils Vor- und Nachteile dargestellt und es wird regelmäßig versucht einen praktischen Zusammenhang herzustellen. Im abschließenden Kapitel 4 soll es im Rahmen einer Performance-Simulationsstudie darum gehen, wie gut sich Minimum-Distanz Schätzer (MD) im Vergleich zu Maximum-Likelihood Schätzern (ML) bei der Parameterbestimmung für Archimedische und Parametrische Copulas verhalten. Dabei werden zunächst die zwei Schätzverfahren vorgestellt, ehe diese anschließend mithilfe des Statistikprogramms R angewendet werden.
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Empirical Likelihood

Author: Art B. Owen

Publisher: CRC Press

ISBN: 1420036157

Category: Mathematics

Page: 304

View: 6010

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 also facilitates incorporating side information, and it simplifies accounting for censored, truncated, or biased sampling. One of the first books published on the subject, Empirical Likelihood offers an in-depth treatment of this method for constructing confidence regions and testing hypotheses. The author applies empirical likelihood to a range of problems, from those as simple as setting a confidence region for a univariate mean under IID sampling, to problems defined through smooth functions of means, regression models, generalized linear models, estimating equations, or kernel smooths, and to sampling with non-identically distributed data. Abundant figures offer visual reinforcement of the concepts and techniques. Examples from a variety of disciplines and detailed descriptions of algorithms-also posted on a companion Web site at-illustrate the methods in practice. Exercises help readers to understand and apply the methods. The method of empirical likelihood is now attracting serious attention from researchers in econometrics and biostatistics, as well as from statisticians. This book is your opportunity to explore its foundations, its advantages, and its application to a myriad of practical problems.
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