Maximum Likelihood Estimation And Inference

Author : Russell B. Millar
Publisher : John Wiley & Sons
Page : 286 pages
File Size : 46,6 Mb
Release : 2011-07-26
Category : Mathematics
ISBN : 9781119977711

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Maximum Likelihood Estimation and Inference by Russell B. Millar Pdf

This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: Provides an accessible introduction to pragmatic maximum likelihood modelling. Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood. Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data. Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology. Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB. Provides all program code and software extensions on a supporting website. Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters. This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter.

Author : Halbert White
Publisher : Cambridge University Press
Page : 396 pages
File Size : 40,9 Mb
Release : 1996-06-28
Category : Business & Economics
ISBN : 0521574463

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Estimation, Inference and Specification Analysis by Halbert White Pdf

This book examines the consequences of misspecifications for the interpretation of likelihood-based methods of statistical estimation and interference. The analysis concludes with an examination of methods by which the possibility of misspecification can be empirically investigated.

Author : Adelchi Azzalini
Publisher : Routledge
Page : 196 pages
File Size : 47,5 Mb
Release : 2017-11-13
Category : Mathematics
ISBN : 9781351414463

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Statistical Inference Based on the likelihood by Adelchi Azzalini Pdf

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.

Author : Raymond L. Chambers,David G. Steel,Suojin Wang,Alan Welsh
Publisher : CRC Press
Page : 391 pages
File Size : 50,6 Mb
Release : 2012-05-02
Category : Mathematics
ISBN : 9781420011357

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Maximum Likelihood Estimation for Sample Surveys by Raymond L. Chambers,David G. Steel,Suojin Wang,Alan Welsh Pdf

Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to

Author : Leonhard Held,Daniel Sabanés Bové
Publisher : Springer Nature
Page : 409 pages
File Size : 42,5 Mb
Release : 2020-03-31
Category : Medical
ISBN : 9783662607923

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Likelihood and Bayesian Inference by Leonhard Held,Daniel Sabanés Bové Pdf

This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

Author : David J. Olive
Publisher : Springer
Page : 434 pages
File Size : 43,9 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9783319049724

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Statistical Theory and Inference by David J. Olive Pdf

This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

Author : Ziding Feng
Publisher : Unknown
Page : 260 pages
File Size : 54,5 Mb
Release : 1990
Category : Electronic
ISBN : CORNELL:31924058943220

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Statistical Inference Using Maximum Likelihood Estimation and the Generalized Likelihood Ratio Under Nonstandard Conditions by Ziding Feng Pdf

Author : Mark J. van der Laan,Sherri Rose
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 45,8 Mb
Release : 2011-06-17
Category : Mathematics
ISBN : 9781441997821

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Targeted Learning by Mark J. van der Laan,Sherri Rose Pdf

The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest. This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.

Author : Yudi Pawitan
Publisher : OUP Oxford
Page : 543 pages
File Size : 51,6 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9780191650581

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In All Likelihood by Yudi Pawitan Pdf

Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.

Author : Ayanendranath Basu,Hiroyuki Shioya,Chanseok Park
Publisher : CRC Press
Page : 429 pages
File Size : 40,6 Mb
Release : 2011-06-22
Category : Computers
ISBN : 9781420099669

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Statistical Inference by Ayanendranath Basu,Hiroyuki Shioya,Chanseok Park Pdf

In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Statistical Inference: The Minimum Distance Approach comprehensively overviews developments in density-based minimum distance inference for independently and identically distributed data. Extensions to other more complex models are also discussed. Comprehensively covering the basics and applications of minimum distance inference, this book introduces and discusses: The estimation and hypothesis testing problems for both discrete and continuous models The robustness properties and the structural geometry of the minimum distance methods The inlier problem and its possible solutions, and the weighted likelihood estimation problem The extension of the minimum distance methodology in interdisciplinary areas, such as neural networks and fuzzy sets, as well as specialized models and problems, including semi-parametric problems, mixture models, grouped data problems, and survival analysis. Statistical Inference: The Minimum Distance Approach gives a thorough account of density-based minimum distance methods and their use in statistical inference. It covers statistical distances, density-based minimum distance methods, discrete and continuous models, asymptotic distributions, robustness, computational issues, residual adjustment functions, graphical descriptions of robustness, penalized and combined distances, weighted likelihood, and multinomial goodness-of-fit tests. This carefully crafted resource is useful to researchers and scientists within and outside the statistics arena.

Author : Leonhard Held,Daniel Sabanés Bové
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 42,6 Mb
Release : 2013-11-12
Category : Mathematics
ISBN : 9783642378874

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Applied Statistical Inference by Leonhard Held,Daniel Sabanés Bové Pdf

This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.

Author : Vance Martin,Stan Hurn,David Harris
Publisher : Cambridge University Press
Page : 925 pages
File Size : 45,6 Mb
Release : 2013
Category : Business & Economics
ISBN : 9780521139816

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Econometric Modelling with Time Series by Vance Martin,Stan Hurn,David Harris Pdf

"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.

Author : Balvant Keshav Kale
Publisher : Alpha Science Int'l Ltd.
Page : 312 pages
File Size : 43,6 Mb
Release : 2005
Category : Business & Economics
ISBN : 1842652192

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A First Course on Parametric Inference by Balvant Keshav Kale Pdf

"After a brief historical perspective, A First Course on Parametric Inference, discusses the basic concept of sufficient statistic and the classical approach based on minimum variance unbiased estimator. There is a separate chapter on simultaneous estimation of several parameters. Large sample theory of estimation, based on consistent asymptotically normal estimators obtained by method of moments, percentile and the method of maximum likelihood is also introduced. The tests of hypotheses for finite samples with classical Neyman-Pearson theory is developed pointing out its connection with Bayesian approach. The hypotheses testing and confidence interval techniques are developed leading to likelihood ratio tests, score tests and tests based on maximum likelihood estimators."--BOOK JACKET.

Author : Michael D. Ward,John S. Ahlquist
Publisher : Cambridge University Press
Page : 327 pages
File Size : 46,7 Mb
Release : 2018-11-22
Category : Political Science
ISBN : 9781107185821

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Maximum Likelihood for Social Science by Michael D. Ward,John S. Ahlquist Pdf

Practical, example-driven introduction to maximum likelihood for the social sciences. Emphasizes computation in R, model selection and interpretation.

Author : Michael R. Kosorok
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 45,7 Mb
Release : 2007-12-29
Category : Mathematics
ISBN : 9780387749785

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Introduction to Empirical Processes and Semiparametric Inference by Michael R. Kosorok Pdf

Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.