No description available.

Thesis (Ph.D.)--University of Texas at Arlington, 2009.

Bibliography: p. 178-182. / The purpose of this thesis is to provide a study of the linear model. The whole work has been split into 6 chapters. In Chapter 1 we define and examine the two linear models, i.e. the regression and the correlation model. More specifically we show that the regression model is the conditional version of the correlation model. In Chapter 2 we deal with the problem of multicollinearity. We investigate the sources of near singularities, we give some methods of detecting the multicollinearity, and we state briefly methods for overcoming this problem. In Chapter 3 we consider the least squares method with restrictions, and we dispose of some tests for testing the linear restrictions. The theory concerning the sign of least squares estimates is discussed, then we deal with the method for augmenting existing data. Chapter 4 is mainly devoted to ridge regression. We state methods for selecting the best estimate for k. Some extensions are given dealing with the shrinkage estimators and the linear transforms of the least squares. In Chapter 5 we deal with the principal components, and we give methods for selecting the best subset of principal components. Much attention was given to a method called fractional rank and latent root regression analysis. In Chapter 6 comparisons were performed between estimators previously mentioned. Finally the conclusions are stated.

Modern data analysis often involves a large number of variables, which gives rise to the problem of multicollinearity in regression models. It is well-known that in a linear model, when the design matrix X is nearly singular, then the ordinary least squares (OLS) estimator may perform poorly because of its numerical instability and large variance. To overcome this problem, many linear or nonlinear biased estimators are studied. In this work we consider a class of generalized shrunken least squares (GSLS) estimators that include many well-known linear biased estimators proposed in the literature. We compare these estimators under the mean square error and matrix mean square error criteria. Moreover, a simulation study and two numerical examples are used to illustrate some of the theoretical results.

Modern data analysis often involves a large number of variables, which gives rise to the problem of multicollinearity in regression models. It is well-known that in a linear model, when the design matrix X is nearly singular, then the ordinary least squares (OLS) estimator may perform poorly because of its numerical instability and large variance. To overcome this problem, many linear or nonlinear biased estimators are studied. In this work we consider a class of generalized shrunken least squares (GSLS) estimators that include many well-known linear biased estimators proposed in the literature. We compare these estimators under the mean square error and matrix mean square error criteria. Moreover, a simulation study and two numerical examples are used to illustrate some of the theoretical results.

La presente tesis está enfocada en los factores que explican el volumen de exportación del café dentro del periodo de 1980 a 2017 en base al área de cultivo, el precio promedio y el rendimiento del café. El propósito de esta investigación es la elaboración de un modelo estadístico que permita a los productores del sector de café pronosticar sus volúmenes de exportación, nuestra metodología consiste en realizar una investigación cuantitativa, con un diseño concluyente no experimental y un alcance descriptivo correlacional. Los resultaron sacaron a relucir que el precio promedio no es una variable significativa que afecte al volumen de exportación, el área cultivada y el rendimiento son los factores primordiales que el productor debe cuidar para aumentar su volumen. El rendimiento del café es una variable muy sensible y en esencia su buen manejo lleva a aumentar significativamente el volumen del productor. / The present thesis is focused on the factors that explain the export volume of coffee in the period from 1980 to 2017 based on the area of cultivation, average price and coffee yield. The purpose of this research is the development of a statistical model that allows producers in the coffee sector to forecast their export volumes, our methodology is to conduct a quantitative research, with a conclusive non-experimental design and a correlational descriptive scope. The results showed that the average price is not a significant variable that affects the export volume, the cultivated area and the yield are the main factors that the producer must take care of to increase its volume. The yield of coffee is a very sensitive variable and in essence its good management leads to significantly increase the volume of the producer. / Tesis

No description available.

Several biased estimators have been proposed as alternatives to the least squares estimator when multicollinearity is present in the multiple linear regression model. Though the ridge estimator and the principal components estimator have been widely used for such problems, it should be noted that their performances in terms of mean square error are dependent upon the orientation of the unknown parameter vector and the magnitude of σ². By defining the fractional principal components regression model as y̲ = Zα̲ + 𝛜̲ = ZF⁻α_F + 𝛜̲ where α_F = Fα̲ and F⁻ is a generalized inverse of a diagonal matrix P, the resulting estimators of α̲_F, based on various forms of F, are shown to define the class of the fractional principal components estimators. In the fractional principal components framework, several new estimation techniques are developed. The performances of the new estimators are evaluated and compared with other commonly used biased estimators both theoretically and by simulation studies. / Ph. D. / incomplete_metadata

Graduation date: 1988

Thesis (M.S.)--Ohio University, November, 1996. / Title from PDF t.p.