Theory Of Statistical Experiments

Author : H. Heyer
Publisher : Springer
Page : 0 pages
File Size : 51,7 Mb
Release : 1982-11-04
Category : Mathematics
ISBN : 0387907858

Get Book

Theory of Statistical Experiments by H. Heyer Pdf

By a statistical experiment we mean the procedure of drawing a sample with the intention of making a decision. The sample values are to be regarded as the values of a random variable defined on some meas urable space, and the decisions made are to be functions of this random variable. Although the roots of this notion of statistical experiment extend back nearly two hundred years, the formal treatment, which involves a description of the possible decision procedures and a conscious attempt to control errors, is of much more recent origin. Building upon the work of R. A. Fisher, J. Neyman and E. S. Pearson formalized many deci sion problems associated with the testing of hypotheses. Later A. Wald gave the first completely general formulation of the problem of statisti cal experimentation and the associated decision theory. These achieve ments rested upon the fortunate fact that the foundations of probability had by then been laid bare, for it appears to be necessary that any such quantitative theory of statistics be based upon probability theory. The present state of this theory has benefited greatly from contri butions by D. Blackwell and L. LeCam whose fundamental articles expanded the mathematical theory of statistical experiments into the field of com parison of experiments. This will be the main motivation for the ap proach to the subject taken in this book.

Author : H. Heyer
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461382188

Get Book

Theory of Statistical Experiments by H. Heyer Pdf

By a statistical experiment we mean the procedure of drawing a sample with the intention of making a decision. The sample values are to be regarded as the values of a random variable defined on some meas urable space, and the decisions made are to be functions of this random variable. Although the roots of this notion of statistical experiment extend back nearly two hundred years, the formal treatment, which involves a description of the possible decision procedures and a conscious attempt to control errors, is of much more recent origin. Building upon the work of R. A. Fisher, J. Neyman and E. S. Pearson formalized many deci sion problems associated with the testing of hypotheses. Later A. Wald gave the first completely general formulation of the problem of statisti cal experimentation and the associated decision theory. These achieve ments rested upon the fortunate fact that the foundations of probability had by then been laid bare, for it appears to be necessary that any such quantitative theory of statistics be based upon probability theory. The present state of this theory has benefited greatly from contri butions by D. Blackwell and L. LeCam whose fundamental articles expanded the mathematical theory of statistical experiments into the field of com parison of experiments. This will be the main motivation for the ap proach to the subject taken in this book.

Author : Helmut Strasser
Publisher : Walter de Gruyter
Page : 505 pages
File Size : 43,8 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110850826

Get Book

Mathematical Theory of Statistics by Helmut Strasser Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : Al?bert Nikolaevich Shiri?aev,V. G. Spokoiny
Publisher : World Scientific
Page : 306 pages
File Size : 51,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9810241011

Get Book

Statistical Experiments and Decisions by Al?bert Nikolaevich Shiri?aev,V. G. Spokoiny Pdf

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is ?how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment?.

Author : D.R. Cox,Nancy Reid
Publisher : CRC Press
Page : 337 pages
File Size : 53,7 Mb
Release : 2000-06-06
Category : Mathematics
ISBN : 9781420035834

Get Book

The Theory of the Design of Experiments by D.R. Cox,Nancy Reid Pdf

Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the spec

Author : Junjirō Ogawa
Publisher : Unknown
Page : 488 pages
File Size : 53,9 Mb
Release : 1974
Category : Science
ISBN : MINN:31951000028239Q

Get Book

Statistical Theory of the Analysis of Experimental Designs by Junjirō Ogawa Pdf

Analysis of variance. The partition of a sum of squares corrected by the mean. Normal theory of distribution problems. Testing the hypothesis on regression coefficients. General linear hypothesis. Analysis of variance in a two-way classification in matrix language. Design of experiments. General remarks. Randomization. Randomized block design. Latin-square design, greco-latin square design. Factorial design. Need for the factorial principle. Fractional replication of a factorial design. Theory of block designs-intrablock analysis. Theory of block designs-interblock analysis. Randomization of partially balanced incomplete block designs.

Author : Ajit C. Tamhane
Publisher : John Wiley & Sons
Page : 720 pages
File Size : 53,6 Mb
Release : 2012-09-12
Category : Science
ISBN : 9781118491430

Get Book

Statistical Analysis of Designed Experiments by Ajit C. Tamhane Pdf

A indispensable guide to understanding and designing modern experiments The tools and techniques of Design of Experiments (DOE) allow researchers to successfully collect, analyze, and interpret data across a wide array of disciplines. Statistical Analysis of Designed Experiments provides a modern and balanced treatment of DOE methodology with thorough coverage of the underlying theory and standard designs of experiments, guiding the reader through applications to research in various fields such as engineering, medicine, business, and the social sciences. The book supplies a foundation for the subject, beginning with basic concepts of DOE and a review of elementary normal theory statistical methods. Subsequent chapters present a uniform, model-based approach to DOE. Each design is presented in a comprehensive format and is accompanied by a motivating example, discussion of the applicability of the design, and a model for its analysis using statistical methods such as graphical plots, analysis of variance (ANOVA), confidence intervals, and hypothesis tests. Numerous theoretical and applied exercises are provided in each chapter, and answers to selected exercises are included at the end of the book. An appendix features three case studies that illustrate the challenges often encountered in real-world experiments, such as randomization, unbalanced data, and outliers. Minitab® software is used to perform analyses throughout the book, and an accompanying FTP site houses additional exercises and data sets. With its breadth of real-world examples and accessible treatment of both theory and applications, Statistical Analysis of Designed Experiments is a valuable book for experimental design courses at the upper-undergraduate and graduate levels. It is also an indispensable reference for practicing statisticians, engineers, and scientists who would like to further their knowledge of DOE.

Author : Michael H. Herzog,Gregory Francis,Aaron Clarke
Publisher : Springer
Page : 146 pages
File Size : 48,8 Mb
Release : 2019-08-13
Category : Science
ISBN : 9783030034993

Get Book

Understanding Statistics and Experimental Design by Michael H. Herzog,Gregory Francis,Aaron Clarke Pdf

This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.

Author : R. Mead
Publisher : Cambridge University Press
Page : 640 pages
File Size : 47,9 Mb
Release : 1990-07-26
Category : Mathematics
ISBN : 0521287626

Get Book

The Design of Experiments by R. Mead Pdf

In all the experimental sciences, good design of experiments is crucial to the success of research. Well-planned experiments can provide a great deal of information efficiently and can be used to test several hypotheses simultaneously. This book is about the statistical principles of good experimental design and is intended for all applied statisticians and practising scientists engaged in the design, implementation and analysis of experiments. Professor Mead has written the book with the emphasis on the logical principles of statistical design and employs a minimum of mathematics. Throughout he assumes that the large-scale analysis of data will be performed by computers and he is thus able to devote more attention to discussions of how all of the available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from medicine, agriculture, industry and other disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design of experiments can make to a scientific project.

Author : Erik Torgersen
Publisher : Cambridge University Press
Page : 706 pages
File Size : 41,7 Mb
Release : 1991-03-14
Category : Business & Economics
ISBN : 0521250307

Get Book

Comparison of Statistical Experiments by Erik Torgersen Pdf

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

Author : A N Shiryaev,V G Spokoiny
Publisher : World Scientific
Page : 300 pages
File Size : 53,8 Mb
Release : 2000-07-04
Category : Mathematics
ISBN : 9789814494151

Get Book

Statistical Experiments and Decisions by A N Shiryaev,V G Spokoiny Pdf

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”. Contents:Statistical Experiments and Their ComparisonConvergence of Statistical Experiments(γ,Γ)-Models. Convergence to (γ,Γ)-ModelsLocal Convergence of Statistical Experiments and Global EstimationStatistical Inference for Autoregressive Models of the First Order Readership: Researchers in probability and statistics. Keywords:Comparison of Statistical Experiments;Mixed Local Asymptotic Normality;Convergence of Experiments;Likelihood Ratio Processes;Contiguity;Autoregressive Models;Minimax Bound;Local Asymptotic NormalityReviews: “It is an interesting, welcome addition to the literature, and it contains many new insights. I congratulate the authors for writing this comprehensive monograph on a difficult subject.” Mathematical Reviews “The book is a highlight in modern mathematical statistics which offers a lot of new concepts. It recalls the brilliant methodology of Le Cam's Theory and the first chapters may be used as introduction into this field.” Mathematics Abstracts

Author : Lucien Le Cam
Publisher : Springer Science & Business Media
Page : 767 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461249467

Get Book

Asymptotic Methods in Statistical Decision Theory by Lucien Le Cam Pdf

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 : Helge Toutenburg,Shalabh
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 50,5 Mb
Release : 2006-05-09
Category : Mathematics
ISBN : 9780387227726

Get Book

Statistical Analysis of Designed Experiments by Helge Toutenburg,Shalabh Pdf

Unique in commencing with relatively simple statistical concepts and ideas found in most introductory statistical textbooks, this book goes on to cover more material useful for undergraduates and graduate in statistics and biostatistics.

Author : Helge Toutenburg,Shalabh
Publisher : Springer Science & Business Media
Page : 615 pages
File Size : 52,6 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9781441911483

Get Book

Statistical Analysis of Designed Experiments, Third Edition by Helge Toutenburg,Shalabh Pdf

This book is the third revised and updated English edition of the German textbook \Versuchsplanung und Modellwahl" by Helge Toutenburg which was based on more than 15 years experience of lectures on the course \- sign of Experiments" at the University of Munich and interactions with the statisticians from industries and other areas of applied sciences and en- neering. This is a type of resource/ reference book which contains statistical methods used by researchers in applied areas. Because of the diverse ex- ples combined with software demonstrations it is also useful as a textbook in more advanced courses, The applications of design of experiments have seen a signi?cant growth in the last few decades in di?erent areas like industries, pharmaceutical sciences, medical sciences, engineering sciences etc. The second edition of this book received appreciation from academicians, teachers, students and applied statisticians. As a consequence, Springer-Verlag invited Helge Toutenburg to revise it and he invited Shalabh for the third edition of the book. In our experience with students, statisticians from industries and - searchers from other ?elds of experimental sciences, we realized the importance of several topics in the design of experiments which will - crease the utility of this book. Moreover we experienced that these topics are mostly explained only theoretically in most of the available books.

Author : Vladimir G. Spokojnyj
Publisher : Unknown
Page : 281 pages
File Size : 51,8 Mb
Release : 1994
Category : Electronic
ISBN : OCLC:722643144

Get Book

Statistical Experiments and Decisions by Vladimir G. Spokojnyj Pdf