Maximum Likelihood Estimation
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Maximum Likelihood Estimation And Inference
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Author : Russell B. Millar
language : en
Publisher: John Wiley & Sons
Release Date : 2011-07-26
Maximum Likelihood Estimation And Inference written by Russell B. Millar 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 2011-07-26 with Mathematics categories.
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.
Maximum Likelihood Estimation
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Author : Scott R. Eliason
language : en
Publisher: SAGE
Release Date : 1993
Maximum Likelihood Estimation written by Scott R. Eliason and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
"Maximum Likelihood Estimation. . . provides a useful introduction. . . it is clear and easy to follow with applications and graphs. . . . I consider this a very useful book. . . . well-written, with a wealth of explanation. . ." --Dougal Hutchison in Educational Research Eliason reveals to the reader the underlying logic and practice of maximum likelihood (ML) estimation 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 (such as the normal error regression model) 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 maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.
Econometric Modelling With Time Series
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Author : Vance Martin
language : en
Publisher: Cambridge University Press
Release Date : 2013
Econometric Modelling With Time Series written by Vance Martin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Business & Economics categories.
"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.
Maximum Likelihood Estimation With Stata Fourth Edition
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Author : William Gould
language : en
Publisher: Stata Press
Release Date : 2010-10-27
Maximum Likelihood Estimation With Stata Fourth Edition written by William Gould and has been published by Stata Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-27 with Mathematics categories.
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.
Maximum Likelihood Estimation For Sample Surveys
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Author : Raymond L. Chambers
language : en
Publisher: CRC Press
Release Date : 2012-05-02
Maximum Likelihood Estimation For Sample Surveys written by Raymond L. Chambers and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-02 with Mathematics categories.
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 biased and inefficient estimates. Maximum Likelihood Estimation for Sample Surveys presents an overview of likelihood methods for the analysis of sample survey data that account for the selection methods used, and includes all necessary background material on likelihood inference. It covers a range of data types, including multilevel data, and is illustrated by many worked examples using tractable and widely used models. It also discusses more advanced topics, such as combining data, non-response, and informative sampling. The book presents and develops a likelihood approach for fitting models to sample survey data. It explores and explains how the approach works in tractable though widely used models for which we can make considerable analytic progress. For less tractable models numerical methods are ultimately needed to compute the score and information functions and to compute the maximum likelihood estimates of the model parameters. For these models, the book shows what has to be done conceptually to develop analyses to the point that numerical methods can be applied. Designed for statisticians who are interested in the general theory of statistics, Maximum Likelihood Estimation for Sample Surveys is also aimed at statisticians focused on fitting models to sample survey data, as well as researchers who study relationships among variables and whose sources of data include surveys.
Statistics For Machine Learning
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Author : Pratap Dangeti
language : en
Publisher: Packt Publishing Ltd
Release Date : 2017-07-21
Statistics For Machine Learning written by Pratap Dangeti and has been published by Packt Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-21 with Computers categories.
Build Machine Learning models with a sound statistical understanding. About This Book Learn about the statistics behind powerful predictive models with p-value, ANOVA, and F- statistics. Implement statistical computations programmatically for supervised and unsupervised learning through K-means clustering. Master the statistical aspect of Machine Learning with the help of this example-rich guide to R and Python. Who This Book Is For This book is intended for developers with little to no background in statistics, who want to implement Machine Learning in their systems. Some programming knowledge in R or Python will be useful. What You Will Learn Understand the Statistical and Machine Learning fundamentals necessary to build models Understand the major differences and parallels between the statistical way and the Machine Learning way to solve problems Learn how to prepare data and feed models by using the appropriate Machine Learning algorithms from the more-than-adequate R and Python packages Analyze the results and tune the model appropriately to your own predictive goals Understand the concepts of required statistics for Machine Learning Introduce yourself to necessary fundamentals required for building supervised & unsupervised deep learning models Learn reinforcement learning and its application in the field of artificial intelligence domain In Detail Complex statistics in Machine Learning worry a lot of developers. Knowing statistics helps you build strong Machine Learning models that are optimized for a given problem statement. This book will teach you all it takes to perform complex statistical computations required for Machine Learning. You will gain information on statistics behind supervised learning, unsupervised learning, reinforcement learning, and more. Understand the real-world examples that discuss the statistical side of Machine Learning and familiarize yourself with it. You will also design programs for performing tasks such as model, parameter fitting, regression, classification, density collection, and more. By the end of the book, you will have mastered the required statistics for Machine Learning and will be able to apply your new skills to any sort of industry problem. Style and approach This practical, step-by-step guide will give you an understanding of the Statistical and Machine Learning fundamentals you'll need to build models.
Foundations Of Modern Econometrics A Unified Approach
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Author : Yongmiao Hong
language : en
Publisher: World Scientific
Release Date : 2020-07-13
Foundations Of Modern Econometrics A Unified Approach written by Yongmiao Hong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-13 with Business & Economics categories.
Modern economies are full of uncertainties and risk. Economics studies resource allocations in an uncertain market environment. As a generally applicable quantitative analytic tool for uncertain events, probability and statistics have been playing an important role in economic research. Econometrics is statistical analysis of economic and financial data. In the past four decades or so, economics has witnessed a so-called 'empirical revolution' in its research paradigm, and as the main methodology in empirical studies in economics, econometrics has been playing an important role. It has become an indispensable part of training in modern economics, business and management.This book develops a coherent set of econometric theory, methods and tools for economic models. It is written as a textbook for graduate students in economics, business, management, statistics, applied mathematics, and related fields. It can also be used as a reference book on econometric theory by scholars who may be interested in both theoretical and applied econometrics.
L Vy Processes
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Author : Ole E Barndorff-Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
L Vy Processes written by Ole E Barndorff-Nielsen 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 2012-12-06 with Mathematics categories.
A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.
The Elements Of Hawkes Processes
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Author : Patrick J. Laub
language : en
Publisher: Springer Nature
Release Date : 2022-01-03
The Elements Of Hawkes Processes written by Patrick J. Laub and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Mathematics categories.
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Quantum State Estimation
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Author : Matteo Paris
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-11
Quantum State Estimation written by Matteo Paris 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 2004-08-11 with Science categories.
This book is a comprehensive survey of most of the theoretical and experimental achievements in the field of quantum estimation of states and operations. Albeit still quite young, this field has already been recognized as a necessary tool for research in quantum optics and quantum information, beyond being a fascinating subject in its own right since it touches upon the conceptual foundations of quantum mechanics. The book consists of twelve extensive lectures that are essentially self-contained and modular, allowing combination of various chapters as a basis for advanced courses and seminars on theoretical or experimental aspects. The last two chapters, for instance, form a self-contained exposition on quantum discrimination problems. The book will benefit graduate students and newcomers to the field as a high-level but accessible textbook, lecturers in search for advanced course material and researchers wishing to consult a modern and authoritative source of reference.