The Combination of Biased and Robust Estimation Techniques in Multiple Regression Models PDF Download

Author: Ronald Gene Askin
Publisher:
ISBN:
Category : Regression analysis
Languages : en
Pages : 434

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Author: James Robert Simpson
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 26

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Author: James R. Simpson
Publisher:
ISBN:
Category :
Languages : en
Pages : 29

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Book Description
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.

Author: Fouad Sabry
Publisher: One Billion Knowledgeable
ISBN:
Category : Computers
Languages : en
Pages : 155

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What is Random Sample Consensus Random sample consensus, also known as RANSAC, is an iterative method that is used to estimate the parameters of a mathematical model based on a collection of observed data that includes outliers. This method is used in situations where the outliers are permitted to have no impact on the values of the estimates. The conclusion is that it is also possible to view it as a tool for detecting outliers. An algorithm is considered to be non-deterministic if it is able to generate a suitable result only with a certain probability, and this likelihood increases as the number of iterations that are permitted via the method increases. In 1981, Fischler and Bolles, who were working at SRI International, were the ones who initially published the algorithm. In order to solve the Location Determination Problem (LDP), which is a problem in which the objective is to find the points in space that project onto an image and then convert those points into a set of landmarks with known positions, they utilized RANSAC. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Random sample consensus Chapter 2: Estimator Chapter 3: Least squares Chapter 4: Outlier Chapter 5: Cross-validation (statistics) Chapter 6: Errors and residuals Chapter 7: Mixture model Chapter 8: Robust statistics Chapter 9: Image stitching Chapter 10: Resampling (statistics) (II) Answering the public top questions about random sample consensus. (III) Real world examples for the usage of random sample consensus in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Random Sample Consensus.

Author: Robert Andersen
Publisher: SAGE
ISBN: 1412940729
Category : Mathematics
Languages : en
Pages : 129

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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.

Author: Yadolah Dodge
Publisher: Springer Science & Business Media
ISBN: 1441987665
Category : Mathematics
Languages : en
Pages : 188

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While there have been a large number of estimation methods proposed and developed for linear regression, none has proved good for all purposes. This text focuses on the construction of an adaptive combination of two estimation methods so as to help users make an objective choice and combine the desirable properties of two estimators.

Author:
Publisher:
ISBN:
Category : Logistics, Naval
Languages : en
Pages : 540

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Author: Ryan Williams
Publisher:
ISBN:
Category :
Languages : en
Pages : 10

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The purpose of this study was to explore the use of robust variance estimation for combining commonly specified multiple regression models and for combining sample-dependent focal slope estimates from diversely specified models. The proposed estimator obviates traditionally required information about the covariance structure of the dependent effect size estimates, making it a potentially flexible method for conducing meta-analyses of regression estimates. A series of Monte Carlo simulations were conducted to explore the performance of the robust variance estimator under different meta-analytic conditions. The results of the simulations for this approach were promising. The robust confidence intervals for each set of parameter combinations were close to nominal probability content in nearly all of the specified conditions. Robust Variance Estimation and Meta-Analysis is appended.

Author: Pavel Cizek
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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The least squares estimator is probably the most frequently used estimation method in regression analysis. Unfortunately, it is also quite sensitive to data contamination and model misspecification. Although there are several robust estimators designed for parametric regression models that can be used in place of least squares, these robust estimators cannot be easily applied to models containing binary and categorical explanatory variables. Therefore, I design a robust estimator that can be used for any linear regression model no matter what kind of explanatory variables the model contains. Additionally, I propose an adaptive procedure that maximizes the efficiency of the proposed estimator for a given data set while preserving its robustness.

Author: Douglas C. Montgomery
Publisher: John Wiley & Sons
ISBN: 1119180171
Category : Mathematics
Languages : en
Pages : 679

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Book Description
Praise for the Fourth Edition "As with previous editions, the authors have produced a leading textbook on regression." —Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.