Author: E.L. Lehmann
Publisher: Springer Nature
ISBN: 3030705781
Category : Mathematics
Languages : en
Pages : 1016
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Book Description
The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
Author: Gökhan Gül
Publisher: Springer
ISBN: 3319492861
Category : Technology & Engineering
Languages : en
Pages : 156
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Book Description
This book generalizes and extends the available theory in robust and decentralized hypothesis testing. In particular, it presents a robust test for modeling errors which is independent from the assumptions that a sufficiently large number of samples is available, and that the distance is the KL-divergence. Here, the distance can be chosen from a much general model, which includes the KL-divergence as a very special case. This is then extended by various means. A minimax robust test that is robust against both outliers as well as modeling errors is presented. Minimax robustness properties of the given tests are also explicitly proven for fixed sample size and sequential probability ratio tests. The theory of robust detection is extended to robust estimation and the theory of robust distributed detection is extended to classes of distributions, which are not necessarily stochastically bounded. It is shown that the quantization functions for the decision rules can also be chosen as non-monotone. Finally, the book describes the derivation of theoretical bounds in minimax decentralized hypothesis testing, which have not yet been known. As a timely report on the state-of-the-art in robust hypothesis testing, this book is mainly intended for postgraduates and researchers in the field of electrical and electronic engineering, statistics and applied probability. Moreover, it may be of interest for students and researchers working in the field of classification, pattern recognition and cognitive radio.
Author: Reinhard Viertl
Publisher: EOLSS Publications
ISBN: 1848260520
Category :
Languages : en
Pages : 410
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Book Description
Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs
Author: I. Paenson
Publisher: Elsevier
ISBN: 1483296210
Category : Mathematics
Languages : en
Pages : 556
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Book Description
Systematic Glossary of the Terminology of Statistical Methods
Author: Bruno Lecoutre
Publisher: Springer
ISBN: 3662440466
Category : Mathematics
Languages : en
Pages : 140
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Book Description
The purpose of this book is not only to revisit the “significance test controversy,”but also to provide a conceptually sounder alternative. As such, it presents a Bayesian framework for a new approach to analyzing and interpreting experimental data. It also prepares students and researchers for reporting on experimental results. Normative aspects: The main views of statistical tests are revisited and the philosophies of Fisher, Neyman-Pearson and Jeffrey are discussed in detail. Descriptive aspects: The misuses of Null Hypothesis Significance Tests are reconsidered in light of Jeffreys’ Bayesian conceptions concerning the role of statistical inference in experimental investigations. Prescriptive aspects: The current effect size and confidence interval reporting practices are presented and seriously questioned. Methodological aspects are carefully discussed and fiducial Bayesian methods are proposed as a more suitable alternative for reporting on experimental results. In closing, basic routine procedures regarding the means and their generalization to the most common ANOVA applications are presented and illustrated. All the calculations discussed can be easily carried out using the freeware LePAC package.
Author: Prakash Gorroochurn
Publisher: John Wiley & Sons
ISBN: 1118063252
Category : Mathematics
Languages : en
Pages : 341
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Book Description
Winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence. "A great book, one that I will certainly add to my personal library." —Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include: Buffon's Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invariance Various paradoxes raised by Joseph Bertrand Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem The Bayesian paradigm and various philosophies of probability Coverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox Classic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.
Author: Lucien Le Cam
Publisher: Springer Science & Business Media
ISBN: 1461249465
Category : Mathematics
Languages : en
Pages : 767
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Book Description
This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.
Author: Daniel Courgeau
Publisher: Springer Science & Business Media
ISBN: 9400728786
Category : Social Science
Languages : en
Pages : 333
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Book Description
This work examines in depth the methodological relationships that probability and statistics have maintained with the social sciences from their emergence. It covers both the history of thought and current methods. First it examines in detail the history of the different paradigms and axioms for probability, from their emergence in the seventeenth century up to the most recent developments of the three major concepts: objective, subjective and logicist probability. It shows the statistical inference they permit, different applications to social sciences and the main problems they encounter. On the other side, from social sciences—particularly population sciences—to probability, it shows the different uses they made of probabilistic concepts during their history, from the seventeenth century, according to their paradigms: cross-sectional, longitudinal, hierarchical, contextual and multilevel approaches. While the ties may have seemed loose at times, they have more often been very close: some advances in probability were driven by the search for answers to questions raised by the social sciences; conversely, the latter have made progress thanks to advances in probability. This dual approach sheds new light on the historical development of the social sciences and probability, and on the enduring relevance of their links. It permits also to solve a number of methodological problems encountered all along their history.
Author: Priscilla E. Greenwood
Publisher: John Wiley & Sons
ISBN: 9780471557791
Category : Mathematics
Languages : en
Pages : 318
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Book Description
The first step-by-step guide to conducting successful Chi-squaredtests Chi-squared testing is one of the most commonly applied statisticaltechniques. It provides reliable answers for researchers in a widerange of fields, including engineering, manufacturing, finance,agriculture, and medicine. A Guide to Chi-Squared Testing brings readers up to date on recentinnovations and important material previously published only in theformer Soviet Union. Its clear, concise treatment and practicaladvice make this an ideal reference for all researchers andconsultants. Authors Priscilla E. Greenwood and Mikhail S. Nikulin demonstratethe application of these general purpose tests in a wide variety ofspecific settings. They also * Detail the various decisions to be made when applying Chi-squaredtests to real data, and the proper application of these tests instandard hypothesis-testing situations * Describe how Chi-squared type tests allow statisticians toconstruct a test statistic whose distribution is asymptoticallyChi-squared, and to compute power against various alternatives * Devote half of the book to examples of Chi-squared tests that canbe easily adapted to situations not covered in the book * Provide a self-contained, accessible treatment of themathematical requisites * Include an extensive bibliography and suggestions for furtherreading
Author: Guido Del Pino
Publisher: Springer
ISBN: 3540470921
Category : Mathematics
Languages : en
Pages : 496
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Book Description
With contributions by numerous experts
