Biased Estimation as a Solution to the Multicollinearity Problem in Multiple Linear Regression
Author: Albert Joseph Klee
Publisher:
Published: 1973
Total Pages: 546
ISBN-13:
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Author: Albert Joseph Klee
Publisher:
Published: 1973
Total Pages: 546
ISBN-13:
DOWNLOAD EBOOKAuthor: Bushra Abdalrasool Ali
Publisher: LAP Lambert Academic Publishing
Published: 2013
Total Pages: 96
ISBN-13: 9783659388736
DOWNLOAD EBOOKThis work deal with biased estimation methods for estimating the parameters of general linear regression model when the data are ill-conditioned. We focus our attention on ordinary and generalized ridge regression estimators, Jackknife ridge estimators and principal components estimators. In chapter one introduction and historical review In chapter two basic concepts, definitions on linear regression model are presented. Moreover, the statistical properties of the ordinary least squares estimators are presented. Classes of biased estimators are discussed in chapter three when the data suffer from the multicollinearity problem. The procedures discussed in the preceding chapters were applied in chapter four to perform the regression analysis employing the data obtained from Midland Refineries Company in Iraq, for 12 years period in order to determine the effect of six different factors on the productivity of labor. The statistical programs, SPSS, and Minitab were employed to perform the required calculations.
Author: Hyoshin Kim
Publisher: Infinite Study
Published:
Total Pages: 15
ISBN-13:
DOWNLOAD EBOOKThis paper proposes an a-level estimation algorithm for ridge fuzzy regression modeling, addressing the multicollinearity phenomenon in the fuzzy linear regression setting.
Author: D. Neeleman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 111
ISBN-13: 9401174865
DOWNLOAD EBOOKIt was R. Frisch, who in his publications 'Correlation and Scatter Analysis in Statistical Variables' (1929) and 'Statistical Confluence Analysis by means of Complete Regression Systems' (1934) first pointed out the complications that arise if one applies regression analysis to variables among which several independent linear relations exist. Should these relationships be exact, then there exist two closely related solutions for this problem, viz. 1. The estimation of 'stable' linear combinations of coefficients, the so-called estimable functions. 2. The dropping of the wen-known condition of unbiasedness of the estimators. This leads to minimum variance minimum bias estimators. This last solution is generalised in this book for the case of a model consisting of several equations. In econometrics however, the relations among variables are nearly always approximately linear so that one cannot apply one of the solutions mentioned above, because in that case the matrices used in these methods are, although ill-conditioned, always of full rank. Approximating these matrices by good-conditioned ones of the desired rank, it is possible to apply these estimation methods. In order to get an insight in the consequences of this approximation a simulation study has been carried out for a two-equation model. Two Stage Least Squares estimators and estimators found with the aid of the above mentioned estimation method have been compared. The results of this study seem to be favourable for this new method.
Author: Arthur Stanley Goldberger
Publisher: Harvard University Press
Published: 1991
Total Pages: 430
ISBN-13: 9780674175440
DOWNLOAD EBOOKThis text prepares first-year graduate students and advanced undergraduates for empirical research in economics, and also equips them for specialization in econometric theory, business, and sociology. A Course in Econometrics is likely to be the text most thoroughly attuned to the needs of your students. Derived from the course taught by Arthur S. Goldberger at the University of Wisconsin-Madison and at Stanford University, it is specifically designed for use over two semesters, offers students the most thorough grounding in introductory statistical inference, and offers a substantial amount of interpretive material. The text brims with insights, strikes a balance between rigor and intuition, and provokes students to form their own critical opinions. A Course in Econometrics thoroughly covers the fundamentals--classical regression and simultaneous equations--and offers clear and logical explorations of asymptotic theory and nonlinear regression. To accommodate students with various levels of preparation, the text opens with a thorough review of statistical concepts and methods, then proceeds to the regression model and its variants. Bold subheadings introduce and highlight key concepts throughout each chapter. Each chapter concludes with a set of exercises specifically designed to reinforce and extend the material covered. Many of the exercises include real microdata analyses, and all are ideally suited to use as homework and test questions.
Author: Steven M. Sidik
Publisher:
Published: 1975
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKAuthor: Phillip Dean Wittmer
Publisher:
Published: 1976
Total Pages: 122
ISBN-13:
DOWNLOAD EBOOKAuthor: Douglas C. Montgomery
Publisher: Wiley-Interscience
Published: 2001-04-16
Total Pages: 680
ISBN-13:
DOWNLOAD EBOOKA comprehensive and thoroughly up-to-date look at regression analysis-still the most widely used technique in statistics today As basic to statistics as the Pythagorean theorem is to geometry, regression analysis is a statistical technique for investigating and modeling the relationship between variables. With far-reaching applications in almost every field, regression analysis is used in engineering, the physical and chemical sciences, economics, management, life and biological sciences, and the social sciences. Clearly balancing theory with applications, Introduction to Linear Regression Analysis describes conventional uses of the technique, as well as less common ones, placing linear regression in the practical context of today's mathematical and scientific research. Beginning with a general introduction to regression modeling, including typical applications, the book then outlines a host of technical tools that form the linear regression analytical arsenal, including: basic inference procedures and introductory aspects of model adequacy checking; how transformations and weighted least squares can be used to resolve problems of model inadequacy; how to deal with influential observations; and polynomial regression models and their variations. Succeeding chapters include detailed coverage of: ? Indicator variables, making the connection between regression and analysis-of-variance modelss ? Variable selection and model-building techniques ? The multicollinearity problem, including its sources, harmful effects, diagnostics, and remedial measures ? Robust regression techniques, including M-estimators, Least Median of Squares, and S-estimation ? Generalized linear models The book also includes material on regression models with autocorrelated errors, bootstrapping regression estimates, classification and regression trees, and regression model validation. Topics not usually found in a linear regression textbook, such as nonlinear regression and generalized linear models, yet critical to engineering students and professionals, have also been included. The new critical role of the computer in regression analysis is reflected in the book's expanded discussion of regression diagnostics, where major analytical procedures now available in contemporary software packages, such as SAS, Minitab, and S-Plus, are detailed. The Appendix now includes ample background material on the theory of linear models underlying regression analysis. Data sets from the book, extensive problem solutions, and software hints are available on the ftp site. For other Wiley books by Doug Montgomery, visit our website at www.wiley.com/college/montgomery.
Author: Michael H. Kutner
Publisher: McGraw-Hill/Irwin
Published: 2005
Total Pages: 1396
ISBN-13: 9780072386882
DOWNLOAD EBOOKLinear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
Author: Esko Leskinen
Publisher:
Published: 1980
Total Pages: 168
ISBN-13:
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