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Robust Regression Estimation Methods And Intercept Bias
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Book Synopsis Robust Regression Estimation Methods and Intercept Bias by : James McDonald
Download or read book Robust Regression Estimation Methods and Intercept Bias written by James McDonald and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust estimation techniques based on symmetric probability distributions are often substituted for OLS to obtain efficient regression parameters with thick-tail distributed data. The empirical, simulation and theoretical results in this paper show that with skewed distributed data, symmetric robust estimation techniques produce biased regression intercepts. This paper evaluates robust methods in estimating the capital asset pricing model and shows skewed stock returns data used with symmetric robust estimation techniques produce biased alphas. The results support the recommendation that robust estimation using the skewed generalized T family of distributions may be used to obtain more efficient and unbiased estimates with skewness.
Book Synopsis Robust Methods in Regression Analysis – Theory and Application by : Robert Finger
Download or read book Robust Methods in Regression Analysis – Theory and Application written by Robert Finger and published by GRIN Verlag. This book was released on 2007-05-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modern Methods for Robust Regression by : Robert Andersen
Download or read book Modern Methods for Robust Regression written by Robert Andersen and published by SAGE. This book was released on 2008 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering an in-depth treatment of robust and resistant regression, this volume takes an applied approach and offers readers empirical examples to illustrate key concepts.
Book Synopsis New Methods and Comparative Evaluations for Robust and Biased- Robust Regression Estimation by : James Robert Simpson
Download or read book New Methods and Comparative Evaluations for Robust and Biased- Robust Regression Estimation written by James Robert Simpson and published by . This book was released on 1995 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Regression by : Kenneth D. Lawrence
Download or read book Robust Regression written by Kenneth D. Lawrence and published by Routledge. This book was released on 2019-05-20 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust Regression: Analysis and Applications characterizes robust estimators in terms of how much they weight each observation discusses generalized properties of Lp-estimators. Includes an algorithm for identifying outliers using least absolute value criterion in regression modeling reviews redescending M-estimators studies Li linear regression proposes the best linear unbiased estimators for fixed parameters and random errors in the mixed linear model summarizes known properties of Li estimators for time series analysis examines ordinary least squares, latent root regression, and a robust regression weighting scheme and evaluates results from five different robust ridge regression estimators.
Book Synopsis Tests for Differences Between Least Squares and Robust Regression Parameter Estimates and Related Topics by : Tatiana A. Maravina
Download or read book Tests for Differences Between Least Squares and Robust Regression Parameter Estimates and Related Topics written by Tatiana A. Maravina and published by . This book was released on 2012 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the present time there is no well accepted test for comparing least squares and robust linear regression coefficient estimates. To fill this gap we propose and demonstrate the efficacy of two Wald-like statistical tests for the above purposes, using for robust regression the class of MM-estimators. The tests are designed to detect significant differences between least squares and robust estimates due to both inefficiency of least squares under fat-tailed non-normality and significantly larger biases of least squares relative to robust regression coefficient estimators under bias inducing distributions. The asymptotic normality of the test statistics is established and the finite sample level and power of the tests are evaluated by Monte Carlo, with the latter yielding promising results. The first part of our research focuses on the LS and robust regression slope estimators, both of which are consistent under skewed error distributions. A second part of the research focuses on intercept estimation, in which case there is a need to adjust for some bias in the robust MM-intercept estimator under skewed error distributions. An interesting by-product of our research is that use of the slowly re-descending Tukey bisquare loss function leads to better test performance than the rapidly re-descending min-max bias optimal loss function.
Book Synopsis Robust Regression and Outlier Detection by : Peter J. Rousseeuw
Download or read book Robust Regression and Outlier Detection written by Peter J. Rousseeuw and published by John Wiley & Sons. This book was released on 2005-02-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "The writing style is clear and informal, and much of thediscussion is oriented to application. In short, the book is akeeper." –Mathematical Geology "I would highly recommend the addition of this book to thelibraries of both students and professionals. It is a usefultextbook for the graduate student, because it emphasizes both thephilosophy and practice of robustness in regression settings, andit provides excellent examples of precise, logical proofs oftheorems. . . .Even for those who are familiar with robustness, thebook will be a good reference because it consolidates the researchin high-breakdown affine equivariant estimators and includes anextensive bibliography in robust regression, outlier diagnostics,and related methods. The aim of this book, the authors tell us, is‘to make robust regression available for everyday statisticalpractice.’ Rousseeuw and Leroy have included all of thenecessary ingredients to make this happen." –Journal of the American Statistical Association
Book Synopsis New Methods and Comparative Evaluations for Robust and Biased- Robust Regression Estimation by : James Robert Simpson
Download or read book New Methods and Comparative Evaluations for Robust and Biased- Robust Regression Estimation written by James Robert Simpson and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Robust Estimation and Hypothesis Testing by : Rand R. Wilcox
Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Academic Press. This book was released on 2012-01-12 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book focuses on the practical aspects of modern and robust statistical methods. The increased accuracy and power of modern methods, versus conventional approaches to the analysis of variance (ANOVA) and regression, is remarkable. Through a combination of theoretical developments, improved and more flexible statistical methods, and the power of the computer, it is now possible to address problems with standard methods that seemed insurmountable only a few years ago"--
Book Synopsis Distributionally Robust Learning by : Ruidi Chen
Download or read book Distributionally Robust Learning written by Ruidi Chen and published by . This book was released on 2020-12-23 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Doing Meta-Analysis with R by : Mathias Harrer
Download or read book Doing Meta-Analysis with R written by Mathias Harrer and published by CRC Press. This book was released on 2021-09-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Meta-Analysis with R: A Hands-On Guide serves as an accessible introduction on how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including calculation and pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced but highly relevant topics such as network meta-analysis, multi-three-level meta-analyses, Bayesian meta-analysis approaches and SEM meta-analysis are also covered. A companion R package, dmetar, is introduced at the beginning of the guide. It contains data sets and several helper functions for the meta and metafor package used in the guide. The programming and statistical background covered in the book are kept at a non-expert level, making the book widely accessible. Features • Contains two introductory chapters on how to set up an R environment and do basic imports/manipulations of meta-analysis data, including exercises • Describes statistical concepts clearly and concisely before applying them in R • Includes step-by-step guidance through the coding required to perform meta-analyses, and a companion R package for the book
Book Synopsis Introduction to Linear Regression Analysis by : Douglas C. Montgomery
Download or read book Introduction to Linear Regression Analysis written by Douglas C. Montgomery and published by Wiley-Interscience. This book was released on 2001-04-16 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 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.
Book Synopsis A Weighted Least Squares Approach to Robustify by : Chowhong Lin
Download or read book A Weighted Least Squares Approach to Robustify written by Chowhong Lin and published by . This book was released on 1998 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Combination of Biased and Robust Estimation Techniques in Multiple Regression Models by : Ronald Gene Askin
Download or read book The Combination of Biased and Robust Estimation Techniques in Multiple Regression Models written by Ronald Gene Askin and published by . This book was released on 1979 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Combined Biased-Robust Estimator for Dealing with Influence and Collinearity in Regression by : James R. Simpson
Download or read book A Combined Biased-Robust Estimator for Dealing with Influence and Collinearity in Regression written by James R. Simpson and published by . This book was released on 1993 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression analysis is a statistical tool that has earned widespread use in nearly all areas of endeavor seeking to fit a model to a set of data, Although there are several methods of estimating the model parameters, the least squares method is used most often because of its general acceptance, elegant statistical properties and ease of computation. Unfortunately, the mathematical elegance that makes least squares so popular depends on a number of fairly strong and many times unrealistic assumptions. The assumption that makes least squares so attractive in terms of hypothesis testing and confidence intervals on the parameter estimates is that the distribution of the errors is normal or Gaussian. This assumption can be violated if one or more sufficiently outlying observations are present in the data, resulting in less than optimal estimates of the parameters. The second problem that can ruin the accuracy of least squares estimates is correlated regressors. Highly correlated regressors can cause large variances in the estimates of the coefficients, sometimes resulting in incorrect levels of magnitude or even incorrect signs for the coefficients. The objective of this research is to develop a biased-robust regression estimator and determine how the method performs in the presence of nonnormal errors (outliers) and multicollinear regressor variables. To accomplish this major objective a number of investigative questions must be answered.
Book Synopsis Handbook of Regression Methods by : Derek Scott Young
Download or read book Handbook of Regression Methods written by Derek Scott Young and published by CRC Press. This book was released on 2018-10-03 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Regression Methods concisely covers numerous traditional, contemporary, and nonstandard regression methods. The handbook provides a broad overview of regression models, diagnostic procedures, and inference procedures, with emphasis on how these methods are applied. The organization of the handbook benefits both practitioners and researchers, who seek either to obtain a quick understanding of regression methods for specialized problems or to expand their own breadth of knowledge of regression topics. This handbook covers classic material about simple linear regression and multiple linear regression, including assumptions, effective visualizations, and inference procedures. It presents an overview of advanced diagnostic tests, remedial strategies, and model selection procedures. Finally, many chapters are devoted to a diverse range of topics, including censored regression, nonlinear regression, generalized linear models, and semiparametric regression. Features Presents a concise overview of a wide range of regression topics not usually covered in a single text Includes over 80 examples using nearly 70 real datasets, with results obtained using R Offers a Shiny app containing all examples, thus allowing access to the source code and the ability to interact with the analyses
Book Synopsis Modern Methods for Robust Regression by : Robert Andersen
Download or read book Modern Methods for Robust Regression written by Robert Andersen and published by SAGE Publications. This book was released on 2007-09-06 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Methods for Robust Regression offers a brief but in-depth treatment of various methods for detecting and properly handling influential cases in regression analysis. This volume, geared toward both future and practicing social scientists, is unique in that it takes an applied approach and offers readers empirical examples to illustrate key concepts. It is ideal for readers who are interested in the issues related to outliers and influential cases. Key Features Defines key terms necessary to understanding the robustness of an estimator: Because they form the basis of robust regression techniques, the book also deals with various measures of location and scale. Addresses the robustness of validity and efficiency: After having described the robustness of validity for an estimator, the author discusses its efficiency. Focuses on the impact of outliers: The book compares the robustness of a wide variety of estimators that attempt to limit the influence of unusual observations. Gives an overview of some traditional techniques: Both formal statistical tests and graphical methods detect influential cases in the general linear model. Offers a Web appendix: This volume provides readers with the data and the R code for the examples used in the book. Intended Audience This is an excellent text for intermediate and advanced Quantitative Methods and Statistics courses offered at the graduate level across the social sciences.
