Parametric Statistical Models And Likelihood

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Parametric Statistical Models and Likelihood

Ole E Barndorff-Nielsen
Parametric Statistical Models and Likelihood Book PDF

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239345

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Parametric Statistical Models and Likelihood by Ole E Barndorff-Nielsen Pdf

This book is a slightly revised and expanded version of a set I I I of notes used for a lecture series given at the Ecole dlEte de I Probabilites at st. Flour in August 1986. In view of the statistical nature of the material discussed herein it was agreed to publish the material as a separate volume in the statistics series rather than, as is the tradition, in a joint volume in the Lecture Notes in Mathematics Series. It is a genuine pleasure to have this opportunity to thank I I I the organizers of Les Ecoles dlEte, and in particular Professor P. -L. Hennequin, for the excellent arrangements of these Summer Schools which form a very significant forum for the exchange of scientific ideas relating to probability. The efficient, careful and patient preparation of the typescript by Oddbj~rg Wethelund is also gratefully acknowledged. Aarhus, June 1988 O. E. Barndorff-Nielsen Parametric statistical Models and Likelihood O. E. Barndorff-Nielsen o. Introduction 0. 1. Outline of contents 1 0. 2. A few preliminaries 2 1. Likelihood and auxiliary statistics 1. 1. Likelihood 4 1. 2. Moments and cumulants of log likelihood derivatives 10 1. 3. Parametrization invariance 13 1. 4. Marginal and conditional likelihood 15 * 1. 5. Combinants, auxiliaries, and the p -model 19 1. 6. Orthogonal parameters 27 1. 7. Pseudo likelihood, profile likelihood and modified 30 profile likelihood 1. 8. Ancillarity and conditionality 33 41 1. 9. Partial sufficiency and partial ancillarity 1. 10.

In All Likelihood

Yudi Pawitan
In All Likelihood Book PDF

Author : Yudi Pawitan
Publisher : OUP Oxford
Page : 543 pages
File Size : 47,9 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.

Parametric Statistical Change Point Analysis

Jie Chen,A.K. Gupta
Parametric Statistical Change Point Analysis Book PDF

Author : Jie Chen,A.K. Gupta
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475731316

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Parametric Statistical Change Point Analysis by Jie Chen,A.K. Gupta Pdf

Recently there has been a keen interest in the statistical analysis of change point detec tion and estimation. Mainly, it is because change point problems can be encountered in many disciplines such as economics, finance, medicine, psychology, geology, litera ture, etc. , and even in our daily lives. From the statistical point of view, a change point is a place or time point such that the observations follow one distribution up to that point and follow another distribution after that point. Multiple change points problem can also be defined similarly. So the change point(s) problem is two fold: one is to de cide if there is any change (often viewed as a hypothesis testing problem), another is to locate the change point when there is a change present (often viewed as an estimation problem). The earliest change point study can be traced back to the 1950s. During the fol lowing period of some forty years, numerous articles have been published in various journals and proceedings. Many of them cover the topic of single change point in the means of a sequence of independently normally distributed random variables. Another popularly covered topic is a change point in regression models such as linear regres sion and autoregression. The methods used are mainly likelihood ratio, nonparametric, and Bayesian. Few authors also considered the change point problem in other model settings such as the gamma and exponential.

Parametric Statistical Inference

James K. Lindsey
Parametric Statistical Inference Book PDF

Author : James K. Lindsey
Publisher : Oxford University Press
Page : 512 pages
File Size : 40,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0198523599

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Parametric Statistical Inference by James K. Lindsey Pdf

Two unifying components of statistics are the likelihood function and the exponential family. These are brought together for the first time as the central themes in this book on statistical inference, written for advanced undergraduate and graduate students in mathematical statistics.

Mathematical Statistics

Richard J. Rossi
Mathematical Statistics Book PDF

Author : Richard J. Rossi
Publisher : John Wiley & Sons
Page : 448 pages
File Size : 47,9 Mb
Release : 2018-06-08
Category : Mathematics
ISBN : 9781118770979

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Mathematical Statistics by Richard J. Rossi Pdf

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.

Non-Standard Parametric Statistical Inference

Russell Cheng
Non Standard Parametric Statistical Inference Book PDF

Author : Russell Cheng
Publisher : Oxford University Press
Page : 432 pages
File Size : 46,8 Mb
Release : 2017-09-15
Category : Mathematics
ISBN : 9780192518316

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Non-Standard Parametric Statistical Inference by Russell Cheng Pdf

This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on: (i) how to recognize situations where the problem is non-standard when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analyzing such problems. A frequentist likelihood-based viewpoint is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically, with only sufficient mathematical detail to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods, as is typically covered in a university statistical inference course, wishing to understand or study how standard methodology might fail. Easy to understand statistical methods are presented which overcome these difficulties, and demonstrated by detailed examples drawn from real applications. Simple and practical model-building is an underlying theme. Parametric bootstrap resampling is used throughout for analyzing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing an accessible demonstration of the sampling behaviour of estimators.

Introduction to Statistical Modelling

Annette J. Dobson
Introduction to Statistical Modelling Book PDF

Author : Annette J. Dobson
Publisher : Springer
Page : 133 pages
File Size : 44,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489931740

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Introduction to Statistical Modelling by Annette J. Dobson Pdf

This book is about generalized linear models as described by NeIder and Wedderburn (1972). This approach provides a unified theoretical and computational framework for the most commonly used statistical methods: regression, analysis of variance and covariance, logistic regression, log-linear models for contingency tables and several more specialized techniques. More advanced expositions of the subject are given by McCullagh and NeIder (1983) and Andersen (1980). The emphasis is on the use of statistical models to investigate substantive questions rather than to produce mathematical descriptions of the data. Therefore parameter estimation and hypothesis testing are stressed. I have assumed that the reader is familiar with the most commonly used statistical concepts and methods and has some basic knowledge of calculus and matrix algebra. Short numerical examples are used to illustrate the main points. In writing this book I have been helped greatly by the comments and criticism of my students and colleagues, especially Anne Young. However, the choice of material, and the obscurities and errors are my responsibility and I apologize to the reader for any irritation caused by them. For typing the manuscript under difficult conditions I am grateful to Anne McKim, Jan Garnsey, Cath Claydon and Julie Latimer.

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935

Anders Hald
A History of Parametric Statistical Inference from Bernoulli to Fisher 1713 1935 Book PDF

Author : Anders Hald
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 44,5 Mb
Release : 2008-08-24
Category : Mathematics
ISBN : 9780387464091

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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 by Anders Hald Pdf

This book offers a detailed history of parametric statistical inference. Covering the period between James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference by inverse probability; the central limit theorem and linear minimum variance estimation by Laplace and Gauss; error theory, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. Lively biographical sketches of many of the main characters are featured throughout, including Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. Also examined are the roles played by DeMoivre, James Bernoulli, and Lagrange.

Complex Data Modeling and Computationally Intensive Statistical Methods

Pietro Mantovan,Piercesare Secchi
Complex Data Modeling and Computationally Intensive Statistical Methods Book PDF

Author : Pietro Mantovan,Piercesare Secchi
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 49,8 Mb
Release : 2011-01-27
Category : Computers
ISBN : 9788847013865

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Complex Data Modeling and Computationally Intensive Statistical Methods by Pietro Mantovan,Piercesare Secchi Pdf

Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.

Methods of Statistical Model Estimation

Joseph Hilbe,Andrew Robinson
Methods of Statistical Model Estimation Book PDF

Author : Joseph Hilbe,Andrew Robinson
Publisher : CRC Press
Page : 255 pages
File Size : 46,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439858035

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Methods of Statistical Model Estimation by Joseph Hilbe,Andrew Robinson Pdf

Methods of Statistical Model Estimation examines the most important and popular methods used to estimate parameters for statistical models and provide informative model summary statistics. Designed for R users, the book is also ideal for anyone wanting to better understand the algorithms used for statistical model fitting.The text presents algorith

Modes of Parametric Statistical Inference

Seymour Geisser,Wesley O. Johnson
Modes of Parametric Statistical Inference Book PDF

Author : Seymour Geisser,Wesley O. Johnson
Publisher : John Wiley & Sons
Page : 218 pages
File Size : 41,7 Mb
Release : 2006-01-27
Category : Mathematics
ISBN : 9780471743125

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Modes of Parametric Statistical Inference by Seymour Geisser,Wesley O. Johnson Pdf

A fascinating investigation into the foundations of statistical inference This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses. The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference: * Frequentist * Likelihood * Fiducial * Bayesian The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development. The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.

Parametric Statistical Inference

Shelemyahu Zacks
Parametric Statistical Inference Book PDF

Author : Shelemyahu Zacks
Publisher : Elsevier
Page : 404 pages
File Size : 46,7 Mb
Release : 2014-05-20
Category : Mathematics
ISBN : 9781483150499

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Parametric Statistical Inference by Shelemyahu Zacks Pdf

Parametric Statistical Inference: Basic Theory and Modern Approaches presents the developments and modern trends in statistical inference to students who do not have advanced mathematical and statistical preparation. The topics discussed in the book are basic and common to many fields of statistical inference and thus serve as a jumping board for in-depth study. The book is organized into eight chapters. Chapter 1 provides an overview of how the theory of statistical inference is presented in subsequent chapters. Chapter 2 briefly discusses statistical distributions and their properties. Chapter 3 is devoted to the problem of sufficient statistics and the information in samples, and Chapter 4 presents some basic results from the theory of testing statistical hypothesis. In Chapter 5, the classical theory of estimation is developed. Chapter 6 discusses the efficiency of estimators and some large sample properties, while Chapter 7 studies the topics on confidence intervals. Finally, Chapter 8 is about decision theoretic and Bayesian approach in testing and estimation. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability will highly benefit from this book.

Targeted Learning

Mark J. van der Laan,Sherri Rose
Targeted Learning Book PDF

Author : Mark J. van der Laan,Sherri Rose
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 48,9 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.

Empirical Likelihood

Art B. Owen
Empirical Likelihood Book PDF

Author : Art B. Owen
Publisher : CRC Press
Page : 324 pages
File Size : 50,6 Mb
Release : 2001-05-18
Category : Mathematics
ISBN : 1420036157

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Empirical Likelihood by Art B. Owen Pdf

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

Statistics with Applications in Biology and Geology

Preben Blaesild,Jorgen Granfeldt
Statistics with Applications in Biology and Geology Book PDF

Author : Preben Blaesild,Jorgen Granfeldt
Publisher : CRC Press
Page : 568 pages
File Size : 44,6 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285888

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Statistics with Applications in Biology and Geology by Preben Blaesild,Jorgen Granfeldt Pdf

The use of statistics is fundamental to many endeavors in biology and geology. For students and professionals in these fields, there is no better way to build a statistical background than to present the concepts and techniques in a context relevant to their interests. Statistics with Applications in Biology and Geology provides a practical introduction to using fundamental parametric statistical models frequently applied to data analysis in biology and geology. Based on material developed for an introductory statistics course and classroom tested for nearly 10 years, this treatment establishes a firm basis in models, the likelihood method, and numeracy. The models addressed include one sample, two samples, one- and two-way analysis of variance, and linear regression for normal data and similar models for binomial, multinomial, and Poisson data. Building on the familiarity developed with those models, the generalized linear models are introduced, making it possible for readers to handle fairly complicated models for both continuous and discrete data. Models for directional data are treated as well. The emphasis is on parametric models, but the book also includes a chapter on the most important nonparametric tests. This presentation incorporates the use of the SAS statistical software package, which authors use to illustrate all of the statistical tools described. However, to reinforce understanding of the basic concepts, calculations for the simplest models are also worked through by hand. SAS programs and the data used in the examples and exercises are available on the Internet.