A Note On Maximum Likelihood Estimators And Nuisance Parameters

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The Theory and Applications of Statistical Interference Functions

Author : D.L. McLeish
Publisher : Springer Science & Business Media
ISBN 13 : 1461238722
Total Pages : 131 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Theory and Applications of Statistical Interference Functions by : D.L. McLeish

Download or read book The Theory and Applications of Statistical Interference Functions written by D.L. McLeish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose out of a desire to develop an approach to statistical infer ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.

Introduction to Empirical Processes and Semiparametric Inference

Author : Michael R. Kosorok
Publisher : Springer Science & Business Media
ISBN 13 : 0387749780
Total Pages : 482 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Introduction to Empirical Processes and Semiparametric Inference by : Michael R. Kosorok

Download or read book Introduction to Empirical Processes and Semiparametric Inference written by Michael R. Kosorok and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Maximum Likelihood Estimation and Inference

Author : Russell B. Millar
Publisher : John Wiley & Sons
ISBN 13 : 1119977711
Total Pages : 286 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Maximum Likelihood Estimation and Inference by : Russell B. Millar

Download or read book Maximum Likelihood Estimation and Inference written by Russell B. Millar and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Targeted Learning

Author : Mark J. van der Laan
Publisher : Springer Science & Business Media
ISBN 13 : 1441997822
Total Pages : 628 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Targeted Learning by : Mark J. van der Laan

Download or read book Targeted Learning written by Mark J. van der Laan and published by Springer Science & Business Media. This book was released on 2011-06-17 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Likelihood Principle

Author : James O. Berger
Publisher : IMS
ISBN 13 : 9780940600133
Total Pages : 266 pages
Book Rating : 4.6/5 (1 download)

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Book Synopsis The Likelihood Principle by : James O. Berger

Download or read book The Likelihood Principle written by James O. Berger and published by IMS. This book was released on 1988 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inference Principles for Biostatisticians

Author : Ian C. Marschner
Publisher : CRC Press
ISBN 13 : 148222223X
Total Pages : 276 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Inference Principles for Biostatisticians by : Ian C. Marschner

Download or read book Inference Principles for Biostatisticians written by Ian C. Marschner and published by CRC Press. This book was released on 2014-12-11 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for students training to become biostatisticians as well as practicing biostatisticians, Inference Principles for Biostatisticians presents the theoretical and conceptual foundations of biostatistics. It covers the theoretical underpinnings essential to understanding subsequent core methodologies in the field. Drawing on his extensive experience teaching graduate-level biostatistics courses and working in the pharmaceutical industry, the author explains the main principles of statistical inference with many examples and exercises. Extended examples illustrate key concepts in depth using a specific biostatistical context. In addition, the author uses simulation to reinforce the repeated sampling interpretation of numerous statistical concepts. Reducing the computational complexities, he provides simple R functions for conducting simulation studies. This text gives graduate students with diverse backgrounds across the health, medical, social, and mathematical sciences a solid, unified foundation in the principles of statistical inference. This groundwork will lead students to develop a thorough understanding of biostatistical methodology.

The Gradient Test

Author : Artur Lemonte
Publisher : Academic Press
ISBN 13 : 0128036133
Total Pages : 157 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis The Gradient Test by : Artur Lemonte

Download or read book The Gradient Test written by Artur Lemonte and published by Academic Press. This book was released on 2016-02-05 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests. Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test. - Covers the background of the gradient statistic and the different models - Discusses The Bartlett-corrected gradient statistic - Explains the algorithm to compute the gradient-type statistic

Probability Theory and Mathematical Statistics

Author : B. Grigelionis
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311231932X
Total Pages : 752 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis Probability Theory and Mathematical Statistics by : B. Grigelionis

Download or read book Probability Theory and Mathematical Statistics written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probability Theory and Mathematical Statistics".

Statistical Estimation for Truncated Exponential Families

Author : Masafumi Akahira
Publisher : Springer
ISBN 13 : 9811052964
Total Pages : 133 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Statistical Estimation for Truncated Exponential Families by : Masafumi Akahira

Download or read book Statistical Estimation for Truncated Exponential Families written by Masafumi Akahira and published by Springer. This book was released on 2017-07-26 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.

Handbook of Latent Variable and Related Models

Author :
Publisher : Elsevier
ISBN 13 : 0080471269
Total Pages : 458 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Latent Variable and Related Models by :

Download or read book Handbook of Latent Variable and Related Models written by and published by Elsevier. This book was released on 2011-08-11 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables. - Covers a wide class of important models - Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data - Includes illustrative examples with real data sets from business, education, medicine, public health and sociology. - Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.

Maximum Likelihood Estimation of Functional Relationships

Author : Nico J.D. Nagelkerke
Publisher : Springer Science & Business Media
ISBN 13 : 1461228581
Total Pages : 118 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Maximum Likelihood Estimation of Functional Relationships by : Nico J.D. Nagelkerke

Download or read book Maximum Likelihood Estimation of Functional Relationships written by Nico J.D. Nagelkerke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of functional relationships concerns itself with inference from models with a more complex error structure than those existing in regression models. We are familiar with the bivariate linear relationship having measurement errors in both variables and the fact that the standard regression estimator of the slope underestimates the true slope. One complication with inference about parameters in functional relationships, is that many of the standard properties of likelihood theory do not apply, at least not in the form in which they apply to e.g. regression models. This is probably one of the reasons why these models are not adequately discussed in most general books on statistics, despite their wide applicability. In this monograph we will explore the properties of likelihood methods in the context of functional relationship models. Full and conditional likelihood methods are both considered. Possible modifications to these methods are considered when necessary. Apart from exloring the theory itself, emphasis shall be placed upon the derivation of useful estimators and their second moment properties. No attempt is made to be mathematically rigid. Proofs are usually outlined with extensive use of the Landau 0(.) and 0(.) notations. It is hoped that this shall provide more insight than the inevitably lengthy proofs meeting strict standards of mathematical rigour.

Monte Carlo Statistical Methods

Author : Christian Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1475741456
Total Pages : 670 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Monte Carlo Statistical Methods by : Christian Robert

Download or read book Monte Carlo Statistical Methods written by Christian Robert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

Principles of Statistical Inference

Author : D. R. Cox
Publisher : Cambridge University Press
ISBN 13 : 1139459139
Total Pages : 227 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Principles of Statistical Inference by : D. R. Cox

Download or read book Principles of Statistical Inference written by D. R. Cox and published by Cambridge University Press. This book was released on 2006-08-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.

Large Sample Techniques for Statistics

Author : Jiming Jiang
Publisher : Springer Science & Business Media
ISBN 13 : 144196827X
Total Pages : 612 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Large Sample Techniques for Statistics by : Jiming Jiang

Download or read book Large Sample Techniques for Statistics written by Jiming Jiang and published by Springer Science & Business Media. This book was released on 2010-06-30 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).

Bayesian Spectrum Analysis and Parameter Estimation

Author : G. Larry Bretthorst
Publisher : Springer Science & Business Media
ISBN 13 : 146849399X
Total Pages : 210 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Bayesian Spectrum Analysis and Parameter Estimation by : G. Larry Bretthorst

Download or read book Bayesian Spectrum Analysis and Parameter Estimation written by G. Larry Bretthorst and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docu ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared.

In All Likelihood

Author : Yudi Pawitan
Publisher : OUP Oxford
ISBN 13 : 0191650587
Total Pages : 626 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis In All Likelihood by : Yudi Pawitan

Download or read book In All Likelihood written by Yudi Pawitan and published by OUP Oxford. This book was released on 2013-01-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Biostatistical Methods

Author : John M. Lachin
Publisher : John Wiley & Sons
ISBN 13 : 1118625846
Total Pages : 676 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Biostatistical Methods by : John M. Lachin

Download or read book Biostatistical Methods written by John M. Lachin and published by John Wiley & Sons. This book was released on 2014-08-22 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . an excellent textbook . . . an indispensable reference for biostatisticians and epidemiologists." —International Statistical Institute A new edition of the definitive guide to classical and modern methods of biostatistics Biostatistics consists of various quantitative techniques that are essential to the description and evaluation of relationships among biologic and medical phenomena. Biostatistical Methods: The Assessment of Relative Risks, Second Edition develops basic concepts and derives an expanded array of biostatistical methods through the application of both classical statistical tools and more modern likelihood-based theories. With its fluid and balanced presentation, the book guides readers through the important statistical methods for the assessment of absolute and relative risks in epidemiologic studies and clinical trials with categorical, count, and event-time data. Presenting a broad scope of coverage and the latest research on the topic, the author begins with categorical data analysis methods for cross-sectional, prospective, and retrospective studies of binary, polychotomous, and ordinal data. Subsequent chapters present modern model-based approaches that include unconditional and conditional logistic regression; Poisson and negative binomial models for count data; and the analysis of event-time data including the Cox proportional hazards model and its generalizations. The book now includes an introduction to mixed models with fixed and random effects as well as expanded methods for evaluation of sample size and power. Additional new topics featured in this Second Edition include: Establishing equivalence and non-inferiority Methods for the analysis of polychotomous and ordinal data, including matched data and the Kappa agreement index Multinomial logistic for polychotomous data and proportional odds models for ordinal data Negative binomial models for count data as an alternative to the Poisson model GEE models for the analysis of longitudinal repeated measures and multivariate observations Throughout the book, SAS is utilized to illustrate applications to numerous real-world examples and case studies. A related website features all the data used in examples and problem sets along with the author's SAS routines. Biostatistical Methods, Second Edition is an excellent book for biostatistics courses at the graduate level. It is also an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.