Advances in Order Restricted Statistical Inference
Advances in Order Restricted Statistical Inference

Author: Richard Dykstra

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 1461399408

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With support from the University of Iowa and the Office of Naval Research. a small conference on order restricted inference was held at the University of Iowa in Iowa City in April of 1981. There were twenty-one participants. mostly from the midwest. and eleven talks were presented. A highlight of the conference was a talk by D. J. Bartholomew on. "Reflections on the past and thoughts about the future. " The conference was especially valuable because it brought together researchers who were thinking about related problems. A small conference on a limited topic is one of the best ways to stimulate research and facilitate collaboration. Because of the success of the first conference. a second conference was organized and held in September of 1985. This second conference was made possible again by support from the Office of Naval Research under Department of the Navy Contract NOOOI4-85-0161 and the University of Iowa. There were thirty-five participants and twenty presentations on a wide variety of topics dealing with order restricted inference at the second conference. This volume is a collection of fourteen of those presentations. By collecting together and organizing the fundamental results in order restricted inference in Statistical Inference under Order Restrictions. R. E. Barlow. D. J. Bartholomew. J. M. Bremner and H. D. Brunk have done much to stimulate research in this area. and so we wish to express our gratitude to them first.

Order Restricted Statistical Inference
Order Restricted Statistical Inference

Author: Tim Robertson

Publisher: John Wiley & Sons Incorporated

Published: 1988

Total Pages: 521

ISBN-13: 9780471917878

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This work attempts to provide a comprehensive treatment of the topic of statistical inference under inequality constraints, in which much of the theory is based on the principles ofr maximum likelihood estimation and likelihood ratio tests.

Statistical Inference as Severe Testing
Statistical Inference as Severe Testing

Author: Deborah G. Mayo

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 503

ISBN-13: 1108563309

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Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.

Statistical Inference Under Order Restrictions
Statistical Inference Under Order Restrictions

Author:

Publisher:

Published: 1972

Total Pages: 388

ISBN-13:

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;Contents: Isotonic regression; Estimation under order restrictions; Testing the equality of ordered means--likelihood ratio tests in the normal case; Testing the equality of ordered means--extensions and generalizations; Estimation of distributions; Isotonic tests for goodness of fit; Conditional expectation given a sigma-lattice.

Constrained Statistical Inference
Constrained Statistical Inference

Author: Mervyn J. Silvapulle

Publisher: John Wiley & Sons

Published: 2011-09-15

Total Pages: 560

ISBN-13: 1118165632

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An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of fields, focusing on sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality-constrained inference problems that do not fit well in the contemplated unified framework, providing a meaningful way for readers to comprehend methodological resolutions. Chapter coverage includes: Population means and isotonic regression Inequality-constrained tests on normal means Tests in general parametric models Likelihood and alternatives Analysis of categorical data Inference on monotone density function, unimodal density function, shape constraints, and DMRL functions Bayesian perspectives, including Stein’s Paradox, shrinkage estimation, and decision theory

Nonparametric Statistical Inference
Nonparametric Statistical Inference

Author: Jean Dickinson Gibbons

Publisher: CRC Press

Published: 2020-12-22

Total Pages: 435

ISBN-13: 1351616161

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Praise for previous editions: "... a classic with a long history." – Statistical Papers "The fact that the first edition of this book was published in 1971 ... [is] testimony to the book’s success over a long period." – ISI Short Book Reviews "... one of the best books available for a theory course on nonparametric statistics. ... very well written and organized ... recommended for teachers and graduate students." – Biometrics "... There is no competitor for this book and its comprehensive development and application of nonparametric methods. Users of one of the earlier editions should certainly consider upgrading to this new edition." – Technometrics "... Useful to students and research workers ... a good textbook for a beginning graduate-level course in nonparametric statistics." – Journal of the American Statistical Association Since its first publication in 1971, Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametrics. The Sixth Edition carries on this tradition and incorporates computer solutions based on R. Features Covers the most commonly used nonparametric procedures States the assumptions, develops the theory behind the procedures, and illustrates the techniques using realistic examples from the social, behavioral, and life sciences Presents tests of hypotheses, confidence-interval estimation, sample size determination, power, and comparisons of competing procedures Includes an Appendix of user-friendly tables needed for solutions to all data-oriented examples Gives examples of computer applications based on R, MINITAB, STATXACT, and SAS Lists over 100 new references Nonparametric Statistical Inference, Sixth Edition, has been thoroughly revised and rewritten to make it more readable and reader-friendly. All of the R solutions are new and make this book much more useful for applications in modern times. It has been updated throughout and contains 100 new citations, including some of the most recent, to make it more current and useful for researchers.

Statistical Inference Based on Divergence Measures
Statistical Inference Based on Divergence Measures

Author: Leandro Pardo

Publisher: CRC Press

Published: 2018-11-12

Total Pages: 513

ISBN-13: 1420034812

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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

The Statistical Analysis of Discrete Data
The Statistical Analysis of Discrete Data

Author: Thomas J. Santner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 381

ISBN-13: 1461210178

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The Statistical Analysis of Discrete Data provides an introduction to cur rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap ply the methods in the text, to explore extensions of the material covered, and to analyze data with discrete responses. In the text examples, and in the problems, we have sought to include interesting data sets from a wide variety of fields including political science, medicine, nuclear engineering, sociology, ecology, cancer research, library science, and biology. Although there are several texts available on discrete data analysis, we felt there was a need for a book which incorporated some of the myriad recent research advances. Our motivation was to introduce the subject by emphasizing its ties to the well-known theories of linear models, experi mental design, and regression diagnostics, as well as to describe alterna tive methodologies (Bayesian, smoothing, etc. ); the latter are based on the premise that external information is available. These overriding goals, to gether with our own experiences and biases, have governed our choice of topics.

Principles of Statistical Inference
Principles of Statistical Inference

Author: D. R. Cox

Publisher: Cambridge University Press

Published: 2006-08-10

Total Pages: 227

ISBN-13: 1139459139

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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.