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An Evaluation Of Ridge Estimators
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Book Synopsis An Evaluation of Ridge Estimators by : Joseph P. Newhouse
Download or read book An Evaluation of Ridge Estimators written by Joseph P. Newhouse and published by . This book was released on 1971 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report explores the statistical properties of a class of estimators, known as either ridge analysis or ridge regression, proposed as an alternative to ordinary least squares (OLS) regression in analyzing sample data that are collinear. Using Monte Carlo techniques, various ridge estimation procedures were evaluated. All the ridge estimators did worse than OLS for at least some choices of the true regression coefficient in the models considered. It thus appears that the ridge estimators proposed to date are not a viable alternative to OLS. However, the results show that it might be possible to define a ridge estimator that would be better than OLS. Until the properties of such an estimator are rigorously derived, the authors caution against using ridge analysis to estimate regression coefficients. (Author).
Book Synopsis An Evaluation of Ridge Regression by : James R. Makin
Download or read book An Evaluation of Ridge Regression written by James R. Makin and published by . This book was released on 1981 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Evaluation of Ridge Regression in Cost Estimation by : James R. Makin (CAPT, USA.)
Download or read book An Evaluation of Ridge Regression in Cost Estimation written by James R. Makin (CAPT, USA.) and published by . This book was released on 1981 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Ridge Regression Estimation with Applications by : A. K. Md. Ehsanes Saleh
Download or read book Theory of Ridge Regression Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2019-01-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis MSE Evaluation of Ridge Regression Using a Pseudo-estimator by : Thomas B. Fomby
Download or read book MSE Evaluation of Ridge Regression Using a Pseudo-estimator written by Thomas B. Fomby and published by . This book was released on 1976 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Kadiyala, K. R Publisher :London, Ont. : Department of Economics, University of Western Ontario ISBN 13 : Total Pages :30 pages Book Rating :4.:/5 (53 download)
Book Synopsis Evaluation of the Mean Squared Error of Certain Generalized Ridge Estimators by : Kadiyala, K. R
Download or read book Evaluation of the Mean Squared Error of Certain Generalized Ridge Estimators written by Kadiyala, K. R and published by London, Ont. : Department of Economics, University of Western Ontario. This book was released on 1978 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Ridge Regression Estimation with Applications by : A. K. Md. Ehsanes Saleh
Download or read book Theory of Ridge Regression Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2019-02-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Monte Carlo Evaluation of Ridge Regression as an Alternative to Ordinary Least Squares by : Bryan Walter Coyle
Download or read book A Monte Carlo Evaluation of Ridge Regression as an Alternative to Ordinary Least Squares written by Bryan Walter Coyle and published by . This book was released on 1979 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ridge Regression Analysis by : Yea-Tsai B. Hsu
Download or read book Ridge Regression Analysis written by Yea-Tsai B. Hsu and published by . This book was released on 1974 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some New Results on Ridge Regression Estimation by : Karl Lin
Download or read book Some New Results on Ridge Regression Estimation written by Karl Lin and published by . This book was released on 1979 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider various interpretations of the ordinary ridge regression estimator with a given shrinkage factor k, and report the results of an extensive Monte Carlo of several ridge regression estimators involving sample-based rules for selecting k. A major distinguishing feature of the study is the use of a general loss structure, the p-norm, in the evaluation process. Other factors taken into consideration include different degree of ill-conditioning of data, different number of explanatory variables, and different shape and non-centrality of the regression coefficients. The main results are: (i) With minor exceptions, all the ridge regression estimators considered yield a smaller average loss regardless of the loss function used. (ii) The reduction in the average loss of the ridge regression estimators increases when the degree ill-conditioning of data increases. The reduction reaches a substantial level when the degree of ill-conditioning is only moderate. (iii) On the basis of our experiment it is possible to make a recomendation concerning the rule of k.
Book Synopsis Ridge Estimators for Probit Regression by : Håkan Locking
Download or read book Ridge Estimators for Probit Regression written by Håkan Locking and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.
Book Synopsis Biased Estimators for Marketing Research by : Lakshman Krishnamurthi
Download or read book Biased Estimators for Marketing Research written by Lakshman Krishnamurthi and published by . This book was released on 1987 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Jackknife, Ridge and Ordinary Least Squares Estimators of Regression Parameters: A Monte Carlo Comparison by : Michael K. Lindell
Download or read book Jackknife, Ridge and Ordinary Least Squares Estimators of Regression Parameters: A Monte Carlo Comparison written by Michael K. Lindell and published by . This book was released on 1979 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study reports the results of a Monte Carlo evaluation of the small sample performance of ordinary least sqares (OLS), ridge and jackknife estimators of regression coefficients. The primary criteria of evaluation are the mean square error (MSE) of the regression coefficients and the size of the t-statistics associated with these coefficients. The conditions studied are derived from a design in which two factors are varied: the sample size to number of predictors (N/p) ratio and the metric quality of the data (dichotomous and polychotomous). Results from 500 replications of each of six cells showed that OLS and jackknife estimators did not differ appreciably on either criterion. Ridge weights had substantially smaller MSE at the lowest levels of N/p (5:1). At high levels of N/p (20:1), ridge weights had a slightly greater MSE than either OLS and jackknifed weights. A dilemma in the use of t-statistics for ridge weights is presented. (Author).
Book Synopsis Improving Efficiency by Shrinkage by : Marvin Gruber
Download or read book Improving Efficiency by Shrinkage written by Marvin Gruber and published by Routledge. This book was released on 2017-11-01 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a treatment of different kinds of James-Stein and ridge regression estimators from a frequentist and Bayesian point of view. The book explains and compares estimators analytically as well as numerically and includes Mathematica and Maple programs used in numerical comparison.;College or university bookshops may order five or more copies at a special student rate, available on request.
Book Synopsis A Monte Carlo Analysis of Principal Components and Ridge Regression with Application to a Fisheries Evaluation Model by : Mary Ellen Sass
Download or read book A Monte Carlo Analysis of Principal Components and Ridge Regression with Application to a Fisheries Evaluation Model written by Mary Ellen Sass and published by . This book was released on 1978 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential to the testing of propositions in economic theory is the estimation of the parameters involved in relationships among economic variables. Probably the most widely used method of estimation is ordinary least squares (OLS). However, severe multicollinearity or near linear dependence of the explanatory variables can cause the OLS estimates to be unrealistic and imprecise due to large sampling variances. One common solution to the multicollinearity problem is to drop highly intercorrelated variables from the regression model. Unfortunately, variable deletion may result in serious specification bias and thus may be a poor method for alleviating multicollinearity. This paper investigates the use of two methods of biased linear estimation, principal components analysis and ridge regression, as alternatives to OLS estimation of the full model in the presence of multicollinearity. A biased linear estimator may be an attractive alternative if its mean square error (MSE) compares favorably with OLS. In this paper, three ridge estimators and two types of principal components estimators are compared to OLS in a series of Monte Carlo experiments and in an application to an empirical problem. The three ridge estimators are: (1) an estimator proposed by Lawless and Wang; (2) a fixed k-value estimator (k = 0.1) ; (3) RIDGM, an estimator proposed by Dempster, Wermuth, et al. The two types of principal components estimators are: (1) the traditional t-criteria for deleting principal components; (2) a proposed loss-function-related criterion for deleting principal components. In the Monte Carlo experiments, OLS and the biased estimators are applied to four data sets, each characterized by a different level of multicollinearity and various information-to-noise ratios. The Monte Carlo results indicate that all the biased estimators can be more effective than OLS (considering MSE) in estimating the parameters of the full model under conditions of high multicollinearity at low and moderate information-to-noise ratios. (The RIDGM estimator, however, produced lower MSE than OLS at all information-to-noise ratios in the data sets where multicollinearity was present.) For principal components analysis, the proposed loss-function-related criterion produced generally lower MSE than the traditional t-criteria. For ridge regression, the Lawless-Wang estimator, which is shown to minimize estimated MSE, produces generally lower MSE than the other ridge estimators in the Monte Carlo experiments. Also, the Lawless-Wang estimator was somewhat more effective overall than the proposed loss-function-related criterion for deleting components. Another comparison of the estimators is made in their application to an empirical problem, a recreation demand model specified by the travel cost method. The comparison of the estimators is based on estimated MSE and on prior information about the coefficients. In this particular case, the Lawless-Wang estimator appears to produce the best improvement over OLS. However, this empirical problem is merely an example of the application of the biased estimators rather than a crucial test of their effectiveness. The inability to judge the reliability of biased estimates, due to the unknown bias squared component of MSE, has been a serious limitation in the application of biased linear estimation to empirical problems. Brown, however, has proposed a method for estimating the MSE of ridge coefficients. His method is applied in the empirical example and in the Monte Carlo experiments to the ridge estimators, and in principle, to the proposed loss-function-related criterion for deleting principal components. For the Lawless-Wang ridge estimator and the proposed loss-function-related criterion, the suggested method for estimating MSE appears to produce good estimates of MSE under conditions of high multicollinearity at low and moderate information-to-noise ratios. In fact, at all but the highest information-to-noise ratio, the Monte Carlo results indicate that this estimate of MSE can be much more accurate than estimates of OLS variances.
Book Synopsis Linear Regression Analysis by : Xin Yan
Download or read book Linear Regression Analysis written by Xin Yan and published by World Scientific. This book was released on 2009 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.
Book Synopsis Preliminary Results of an Evaluation of the Utility of Ridge Regression for Making County Population Estimates by : David A. Swanson
Download or read book Preliminary Results of an Evaluation of the Utility of Ridge Regression for Making County Population Estimates written by David A. Swanson and published by . This book was released on 1977 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
