Statistical Inference Based On The Likelihood
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Statistical Inference Based On The Likelihood
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Author : Adelchi Azzalini
language : en
Publisher: Routledge
Release Date : 2017-11-13
Statistical Inference Based On The Likelihood written by Adelchi Azzalini and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-13 with Mathematics categories.
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.
Statistical Inference Based On Divergence Measures
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Author : Leandro Pardo
language : en
Publisher: CRC Press
Release Date : 2018-11-12
Statistical Inference Based On Divergence Measures written by Leandro Pardo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-12 with Mathematics categories.
The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this p
Applied Statistical Inference
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Author : Leonhard Held
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-12
Applied Statistical Inference written by Leonhard Held and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-12 with Mathematics categories.
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.
Principles Of Statistical Inference
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Author : Luigi Pace
language : en
Publisher: World Scientific
Release Date : 1997-08-05
Principles Of Statistical Inference written by Luigi Pace and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-05 with Mathematics categories.
In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
Statistical Inference
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Author : S.D. Silvey
language : en
Publisher: Routledge
Release Date : 2017-10-19
Statistical Inference written by S.D. Silvey and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Statistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions
Mathematical Statistics
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Author : Richard J. Rossi
language : en
Publisher: John Wiley & Sons
Release Date : 2018-06-08
Mathematical Statistics written by Richard J. Rossi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-08 with Mathematics categories.
Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.
Statistical Inference Based On Ranks
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Author : Thomas P. Hettmansperger
language : en
Publisher:
Release Date : 1991
Statistical Inference Based On Ranks written by Thomas P. Hettmansperger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Some Basic Theory For Statistical Inference
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Author : E.J.G. Pitman
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Some Basic Theory For Statistical Inference written by E.J.G. Pitman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
In this book the author presents with elegance and precision some of the basic mathematical theory required for statistical inference at a level which will make it readable by most students of statistics.
Statistical Inference
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Author : Ayanendranath Basu
language : en
Publisher: CRC Press
Release Date : 2011-06-22
Statistical Inference written by Ayanendranath Basu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-22 with Computers categories.
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, Stati
Probability And Statistical Inference
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Author : Miltiadis C. Mavrakakis
language : en
Publisher: CRC Press
Release Date : 2021-03-28
Probability And Statistical Inference written by Miltiadis C. Mavrakakis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-28 with Mathematics categories.
Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting. Features: •Complete introduction to mathematical probability, random variables, and distribution theory. •Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes. •Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference. •Detailed introduction to Bayesian statistics and associated topics. •Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC). This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.