[PDF] Ridge Fuzzy Regression Modelling For Solving Multicollinearity eBook

Author : Hyoshin Kim
Publisher : Infinite Study
Page : 15 pages
File Size : 42,73 MB
Release :
Category : Mathematics
ISBN :

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This paper proposes an a-level estimation algorithm for ridge fuzzy regression modeling, addressing the multicollinearity phenomenon in the fuzzy linear regression setting.

Author : Janusz Kacprzyk
Publisher : Physica
Page : 302 pages
File Size : 45,72 MB
Release : 1992-08-27
Category : Business & Economics
ISBN :

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Regression analysis is a relatively simple yet extremely useful and widely employed tool for determining relationship between some variables on the basis of some observed values taken by these variables. Fuzzy regression analysis has been recently deviced to accomodate in the framework of regression analysis vaguely specified data which are omnipresent in many applications, notably in all areas where human judgements are used. Fuzzy sets theory provides here proper tools. This book is a collection of papers written by virtually all major contributors to fuzzy regression. Its main issue is that vague, imprecise, etc. data may now be used in regression analysis. This is new. Apart from this it gives an extensive coverage of the whole field of fuzzy regression, both in a strictly mathematical and applicational perspective. Most approaches are algorithmic, and can be readily implemented. Information on software is provided.

Author : Vlassios Hrissanthou
Publisher : Nova Science Publishers
Page : 342 pages
File Size : 10,40 MB
Release : 2018-08
Category : MATHEMATICS
ISBN : 9781536137996

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"Aims to present both conventional and fuzzy regression analyses from theoretical aspects followed by application examples. The present book contains chapters originating from different scientific fields. The first deals with both crisp (conventional) linear or nonlinear regression and fuzzy linear or nonlinear regression. The application example refers to the relationship between sediment transport rates on the one hand and stream discharge and rainfall intensity on the other hand. Second chapter refers to the crisp linear or nonlinear regression of six heavy metals between different soft tissues and shells of Telescopium telescopium and its habitat surface sediments. Third describes the crisp linear, multiple linear, nonlinear and Gaussian process regressions. The fourth is confronted with a classic regression model, named Geographically Weighted Regression (GWR), which constitutes a spatial statistics method. The fifth chapter regards fuzzy linear regression based on symmetric triangular fuzzy numbers. The sixth chapter treats fuzzy linear regression based on trapezoidal membership functions. The main application of this chapter concerns the dependence of rainfall records between neighboring rainfall stations for a small sample of data. The next chapter refers to the multivariable crisp and fuzzy linear regression. The eighth chapter deals with the fuzzy linear regression, with crisp input data and fuzzy output data. All the chapters offer a proper foundation of either widely used or new techniques upon regression. Among the new techniques, several innovated fuzzy regression based methodologies are developed for real problems, and useful conclusions are drawn"--

Author : James R. Makin
Publisher :
Page : 105 pages
File Size : 21,30 MB
Release : 1981
Category :
ISBN :

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The technique of linear regression has been applied as a tool for predicting the cost of an item based on its most important characteristics. Often these characteristics (variables) tend to be highly intercorrelated (the data are said to exhibit multicollinearity) causing least squares estimates of the regression coefficients to be unstable and possibly leading to erroneous predictions. Ridge regression, a possible remedy for the problems caused by multicollinearity proposed by Hoerl and Kennard, is a biased estimation technique which reduces the variance of estimators and provides more precision (as measured by mean square error of the coefficients) than ordinary least squares (OLS) estimators. A comparison was made between these techniques to determine when ridge regression provides better cost equation coefficient estimates than OLS as a function of the degree of multicollinearity in the data, the number of predictor variables in the model, the degree of model fit (R2), and the amount of bias (k) of the estimate. A regression analysis of both sets showed that the degree of multicollinearity and amount of bias interact in explaining the major part of the improvement (degradation) in the mean square coefficient error.

Author : A. K. Md. Ehsanes Saleh
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 29,80 MB
Release : 2019-01-08
Category : Mathematics
ISBN : 1118644522

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A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.