Some Properties of the Least Squares Estimator in Regression Analysis when the Independent Variables are Stochastic PDF Download
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Author: P. K. Bhattacharya (Mathematician)
Publisher:
ISBN:
Category : Matrices
Languages : en
Pages : 32
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Book Description
For the linear regression of y on x observations the loss in estimating the true regression function by another function is considered as a loss function. For the loss function, it is shown under certain conditions that if the class of estimates which are linear in y's and have bounded risk is non-empty, then the estimate obtained by the method of least squares belongs to this class and has uniformly minimum risk in this class. A necessary and sufficient condition on the distribution function of x observations is obtained for this class to be non-empty, which unfortunately is not easy to verify in particular cases and is violated in a ver simple situation. owever, by a sequential modification of the sampling scheme, this condition may always be satisfied at the cost of an arbitrarily small increase in the expected sa ple size. I T IS ALSO SHOWN UNDER CERTAIN FURTHER C NDITIONS ON THE FAMILY OF ADMISSIBLE DISTRIB TIONS THAT THE LEAST SQUARES ESTIMATOR IS MINIMAX IN THE CLASS OF ALL ESTIMATORS. (Author).
Author: P. K. Bhattacharya (Mathematician)
Publisher:
ISBN:
Category : Matrices
Languages : en
Pages : 32
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Book Description
For the linear regression of y on x observations the loss in estimating the true regression function by another function is considered as a loss function. For the loss function, it is shown under certain conditions that if the class of estimates which are linear in y's and have bounded risk is non-empty, then the estimate obtained by the method of least squares belongs to this class and has uniformly minimum risk in this class. A necessary and sufficient condition on the distribution function of x observations is obtained for this class to be non-empty, which unfortunately is not easy to verify in particular cases and is violated in a ver simple situation. owever, by a sequential modification of the sampling scheme, this condition may always be satisfied at the cost of an arbitrarily small increase in the expected sa ple size. I T IS ALSO SHOWN UNDER CERTAIN FURTHER C NDITIONS ON THE FAMILY OF ADMISSIBLE DISTRIB TIONS THAT THE LEAST SQUARES ESTIMATOR IS MINIMAX IN THE CLASS OF ALL ESTIMATORS. (Author).
Author: Denzil G. Fiebig
Publisher:
ISBN:
Category : Least squares
Languages : en
Pages : 44
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Book Description
Author: R. Carter Hill
Publisher: John Wiley & Sons
ISBN: 1118452275
Category : Business & Economics
Languages : en
Pages : 1808
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Book Description
Principles of Econometrics, Fifth Edition, is an introductory book for undergraduate students in economics and finance, as well as first-year graduate students in a variety of fields that include economics, finance, accounting, marketing, public policy, sociology, law, and political science. Students will gain a working knowledge of basic econometrics so they can apply modeling, estimation, inference, and forecasting techniques when working with real-world economic problems. Readers will also gain an understanding of econometrics that allows them to critically evaluate the results of others’ economic research and modeling, and that will serve as a foundation for further study of the field. This new edition of the highly-regarded econometrics text includes major revisions that both reorganize the content and present students with plentiful opportunities to practice what they have read in the form of chapter-end exercises.
Author: Alexander Holmes
Publisher:
ISBN: 9781998109487
Category :
Languages : en
Pages : 0
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Book Description
Printed in b&w. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.
Author: Edward W. Frees
Publisher: Cambridge University Press
ISBN: 9780521535380
Category : Business & Economics
Languages : en
Pages : 492
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Book Description
An introduction to foundations and applications for quantitatively oriented graduate social-science students and individual researchers.
Author:
Publisher: SAGE Publications
ISBN: 1544336586
Category : GAUSS
Languages : en
Pages : 273
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Book Description
Least squares estimation.
Author:
Publisher:
ISBN:
Category : Health surveys
Languages : en
Pages : 524
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Book Description
Author: Richard A. Johnson
Publisher: John Wiley & Sons
ISBN: 0470409274
Category : Mathematics
Languages : en
Pages : 712
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Book Description
Johnson provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters have been updated with real-world data to make the material more relevant. The revised pedagogy will help them contextualize statistical concepts and procedures. The numerous examples clearly demonstrate the important points of the methods. New What Will We Learn opening paragraphs set the stage for the material being discussed. Using Statistics Wisely boxes summarize key lessons. In addition, Statistics in Context sections give business professionals an understanding of applications in which a statistical approach to variation is needed.
Author: Robert Finger
Publisher: GRIN Verlag
ISBN: 3638634507
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Diploma Thesis from the year 2006 in the subject Mathematics - Statistics, grade: 1.3, European University Viadrina Frankfurt (Oder) (Wirtschaftswissenschaftliche Fakultät), language: English, abstract: Regression Analysis is an important statistical tool for many applications. The most frequently used approach to Regression Analysis is the method of Ordinary Least Squares. But this method is vulnerable to outliers; even a single outlier can spoil the estimation completely. How can this vulnerability be described by theoretical concepts and are there alternatives? This thesis gives an overview over concepts and alternative approaches. The three fundamental approaches to Robustness (qualitative-, infinitesimal- and quantitative Robustness) are introduced in this thesis and are applied to different estimators. The estimators under study are measures of location, scale and regression. The Robustness approaches are important for the theoretical judgement of certain estimators but as well for the development of alternatives to classical estimators. This thesis focuses on the (Robustness-) performance of estimators if outliers occur within the data set. Measures of location and scale provide necessary steppingstones into the topic of Regression Analysis. In particular the median and trimming approaches are found to produce very robust results. These results are used in Regression Analysis to find alternatives to the method of Ordinary Least Squares. Its vulnerability can be overcome by applying the methods of Least Median of Squares or Least Trimmed Squares. Different outlier diagnostic tools are introduced to improve the poor efficiency of these Regression Techniques. Furthermore, this thesis delivers a simulation of some Regression Techniques on different situations in Regression Analysis. This simulation focuses in particular on changes in regression estimates if outliers occur in the data. Theoretically derived results as well as the results of the simulation lead to the recommendation of the method of Reweighted Least Squares. Applying this method frequently on problems of Regression Analysis provides outlier resistant and efficient estimates.
Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574
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Book Description
