The Problem Of Estimation
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The Problem Of Estimation
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Author : Correa Moylan Walsh
language : en
Publisher: CreateSpace
Release Date : 2015-01-11
The Problem Of Estimation written by Correa Moylan Walsh and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-11 with Business & Economics categories.
As Reviewed by Irving Fisher Mr. Walsh is the author of "The Measurement of General Exchange Value," one of the chief classics on the subject of index numbers. The present book is partly a condensation of "The Measurement of General Exchange Value," and partly an extension of its ideas to other problems than that of index numbers. Nevertheless the chief interest in the present volume centers, I think, in the author's discussion of index numbers. It is largely taken up with a discussion of the geometric mean as contrasted with other means. Mr. Walsh has delved deep in the lore to be found in libraries on the subject and has unearthed an interesting old discussion of Galileo on "the problem of estimation." Mr. Walsh begins his book by giving the arguments of Galileo and his opponent, which are very entertaining. This old problem reads "if a horse worth 100 pounds is estimated by one person at 1000 and by another at 10, which of these two estimates is the less erroneous, or are they equally erroneous?” According to one view 10 is much nearer the truth (100) than is 1000, the difference in the first case being 90 and in the second, 900. According to another view they are equally distant, one being 10 times as large and the other 10 times as little! Galileo took the latter view and Walsh approves. In the part devoted to index numbers, Walsh (page 102) confirms my views expressed in the March Number of the Quarterly Publications of the American Statistical Association on the best formula for an index number although his method of arriving at the result is quite different from my own. It is interesting to observe that Allyn Young of Harvard in the August number of the Quarterly Journal of Economics in an article entitled “The Measurement of Changes of the General Price Level,” has reached the same result from a different angle. Walsh's argument is largely that the formula in question comes nearest to satisfying Westergaard's test, that is the so-called circular test that any index number should, if calculated from one year to another and from the second to a third and so on in a chain, give the same result as though calculated directly from the original base to the last year. In my forthcoming book on Index Numbers, to be published by the Pollak Foundation for Economic Research, I propose to show that, while index numbers which come near to satisfying Westergaard's test are better than those which fall far short of satisfying it, nevertheless there is an irreducible minimum of discrepancy which is not only inevitable in good index numbers but commendable. Much of Walsh's work in index numbers has been in the search for a formula which will completely fulfill Westergaard's test. The truth is that no such formula exists; at least not one which has different weights for each year to year comparison. But the search for such fulfillment, while in vain in the sense of being unsuccessful in its object, has nevertheless not been fruitless; for Walsh has laid secure foundations in this subject, which he was enabled to lay by virtue of his search for the impossible.
The Problem Of Estimation
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Author : Correa Moylan Walsh
language : en
Publisher:
Release Date : 1921
The Problem Of Estimation written by Correa Moylan Walsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1921 with Economics, Mathematical categories.
Foundations Of Estimation Theory
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Author : L. Kubacek
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Foundations Of Estimation Theory written by L. Kubacek and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapters on linear and quadratic estimations, and normality of observation vectors have been included. Chapter 2 includes selected items of information from algebra, functional analysis and the theory of probability, intended to facilitate the reading of the text proper and to save the reader looking up individual theorems in various textbooks and papers; it is mainly devoted to the reproducing kernel Hilbert spaces, helpful in solving many estimation problems. The text proper of the book begins with Chapter 3. This is divided into two parts: the first deals with sufficient statistics, complete sufficient statistics, minimal sufficient statistics and relations between them; the second contains the mostimportant inequalities of estimation theory for scalar and vector valued parameters and presents properties of the exponential family of distributions.The fourth chapter is an introduction to asymptotic methods of estimation. The method of statistical moments and the maximum-likelihood method are investigated. The sufficient conditions for asymptotical normality of the estimators are given for both methods. The linear and quadratic methods of estimation are dealt with in the fifth chapter. The method of least squares estimation is treated. Five basic regular versions of the regression model and the unified linear model of estimation are described. Unbiased estimators for unit dispersion (factor of the covariance matrix) are given for all mentioned cases. The equivalence of the least-squares method to the method of generalized minimum norm inversion of the design matrix of the regression model is studied in detail. The problem of estimating the covariance components in the mixed model is mentioned as well. Statistical properties of linear and quadratic estimators developed in the fifth chapter in the case of normally distributed errors of measurement are given in Chapter 6. Further, the application of tensor products of Hilbert spaces generated by the covariance matrix of random error vector of observations is demonstrated. Chapter 7 reviews some further important methods of estimation theory. In the first part Wald's method of decision functions is applied to the construction of estimators. The method of contracted estimators and the method of Hoerl and Kennard are presented in the second part. The basic ideas of robustness and Bahadur's approach to estimation theory are presented in the third and fourth parts of this last chapter.
The Problem Of Estimation
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Author : Correa Moylan Walsh
language : en
Publisher: Forgotten Books
Release Date : 2017-12-19
The Problem Of Estimation written by Correa Moylan Walsh and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
Excerpt from The Problem of Estimation: A Seventeenth-Century Controversy and Its Bearing on Modern Statistical Questions, Especially Index-Numbers This little work has been written in the interest of harmony. In mathematics disputes must soon come to an end, when the one side is proved and the other disproved. And where mathematics enter into economics, it would seem that little room could be left for long-continued disputation. It is therefore somewhat surprising that one economist after another takes up the subject of index-numbers, potters over it for a while, differs from the rest if he can, and then drops it. And so nearly sixty years have gone by since Jevons first brought mathe'tnatics to bear upon this question, and still economists are at loggerheads over it. Yet index numbers involve the use of means and averages, and these being a purely mathematical element, demonstration ought soon to be reached, and then agreement should speedily follow. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Estimation Of Mean In Presence Of Non Response Using Exponential Estimator
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Author : Rajesh Singh
language : en
Publisher: Infinite Study
Release Date :
Estimation Of Mean In Presence Of Non Response Using Exponential Estimator written by Rajesh Singh and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This paper considers the problem of estimating the population mean using information on auxiliary variable in presence of non response. Exponential ratio and exponential product type estimators have been suggested and their properties are studied. An empirical study is carried out to support the theoretical results.
Introduction To Variance Estimation
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Author : Kirk Wolter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-14
Introduction To Variance Estimation written by Kirk Wolter 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 2003-11-14 with Education categories.
Now available in paperback, this book is organized in a way that emphasizes both the theory and applications of the various variance estimating techniques. Results are often presented in the form of theorems; proofs are deleted when trivial or when a reference is readily available. It applies to large, complex surveys; and to provide an easy reference for the survey researcher who is faced with the problem of estimating variances for real survey data.
Introduction To Variance Estimation
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Author : Kirk Wolter
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-13
Introduction To Variance Estimation written by Kirk Wolter 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 2007-08-13 with Mathematics categories.
Now available in paperback, this book is organized in a way that emphasizes both the theory and applications of the various variance estimating techniques. Results are often presented in the form of theorems; proofs are deleted when trivial or when a reference is readily available. It applies to large, complex surveys; and to provide an easy reference for the survey researcher who is faced with the problem of estimating variances for real survey data.
Parameter Estimation And Inverse Problems
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Author : Richard C. Aster
language : en
Publisher: Elsevier
Release Date : 2018-10-16
Parameter Estimation And Inverse Problems written by Richard C. Aster and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-16 with Science categories.
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner
Estimation And Inferential Statistics
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Author : Pradip Kumar Sahu
language : en
Publisher: Springer
Release Date : 2015-11-03
Estimation And Inferential Statistics written by Pradip Kumar Sahu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-03 with Mathematics categories.
This book focuses on the meaning of statistical inference and estimation. Statistical inference is concerned with the problems of estimation of population parameters and testing hypotheses. Primarily aimed at undergraduate and postgraduate students of statistics, the book is also useful to professionals and researchers in statistical, medical, social and other disciplines. It discusses current methodological techniques used in statistics and related interdisciplinary areas. Every concept is supported with relevant research examples to help readers to find the most suitable application. Statistical tools have been presented by using real-life examples, removing the “fear factor” usually associated with this complex subject. The book will help readers to discover diverse perspectives of statistical theory followed by relevant worked-out examples. Keeping in mind the needs of readers, as well as constantly changing scenarios, the material is presented in an easy-to-understand form.
Guaranteed Estimation Problems In The Theory Of Linear Ordinary Differential Equations With Uncertain Data
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Author : Oleksandr Nakonechnyi
language : en
Publisher: CRC Press
Release Date : 2022-09-01
Guaranteed Estimation Problems In The Theory Of Linear Ordinary Differential Equations With Uncertain Data written by Oleksandr Nakonechnyi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Mathematics categories.
This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.