Parametric regression fitting (such as OLS) to a data set requires specification of an underlying model. If the specified model is different from the true model, then the parametric fit suffers to a degree that varies with the extent of model misspecification. Mays and Birch (1996) addressed this problem in the one regressor variable case with a method known as Model Robust Regression (MRR), which is a weighted average of independent parametric and nonparametric fits to the data. This paper was based on the underlying assumption of "well-behaved" (Normal) data. The method seeks to take advantage of the beneficial aspects of the both techniques: the parametric, which makes use of the prior knowledge of the researcher via a specified model, and the nonparametric, which is not restricted by a (possibly misspecified) underlying model. The method introduced here (termed Outlier Resistant Model Robust Regression (ORMRR)) addresses the situation that arises when one cannot assume well-behaved data that vary according to a Normal distribution. ORMRR is a blend of a robust parametric fit, such as M-estimation, with a robust nonparametric fit, such as Loess. Some properties of the method will be discussed as well as illustrated with several examples. / Ph. D.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed July 9, 2007). PDF text:180 p. : ill. (some col.) UMI publication number: AAT 3250075. Includes bibliographical references. Also available in microfilm and microfiche formats.

No description available.

A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 136-141).

Thesis (Ph. D.)--University of Jyväskylä. / Extra t.p., with thesis statement, inserted. Summary in Finnish. Includes bibliographical references (p. 113-115).

This paper aims to demonstrate the benefits of adopting a nonparametric regression approach when the standard regression model is not appropriate; it also provides an overview of circumstances where a nonparametric approach might not only be beneficial, but necessary. It begins with a historical background on regression, leading into a broad discussion of the standard linear regression model assumptions. Following are particular methods to handle assumption violations which include nonlinear transformations, nonlinear parametric model fitting, and, finally, nonparametric methods. The software package, R, is used to illustrate examples of nonparametric regression techniques for continuous variables and a brief overview is given of procedures to handle nonparametric regression models that include categorical variables. / text

No description available.

No description available.