Regression models are often transformed into certain alternative forms in statistical inference theory.In this paper,we assume that a general linear model(GLM)is transformed into two diferent forms,and our aim is to s...Regression models are often transformed into certain alternative forms in statistical inference theory.In this paper,we assume that a general linear model(GLM)is transformed into two diferent forms,and our aim is to study some comparison problems under the two transformed general linear models(TGLMs).We frst construct a general vector composed of all unknown parameters under the two diferent TGLMs,derive exact expressions of best linear minimum bias predictors(BLMBPs)by solving a constrained quadratic matrix-valued function optimization problem in the L¨owner partial ordering,and describe a variety of mathematical and statistical properties and performances of the BLMBPs.We then approach some algebraic characterization problems concerning relationships between the BLMBPs under two diferent TGLMs.As applications,two specifc cases are presented to illustrate the main contributions in the study.展开更多
文摘Regression models are often transformed into certain alternative forms in statistical inference theory.In this paper,we assume that a general linear model(GLM)is transformed into two diferent forms,and our aim is to study some comparison problems under the two transformed general linear models(TGLMs).We frst construct a general vector composed of all unknown parameters under the two diferent TGLMs,derive exact expressions of best linear minimum bias predictors(BLMBPs)by solving a constrained quadratic matrix-valued function optimization problem in the L¨owner partial ordering,and describe a variety of mathematical and statistical properties and performances of the BLMBPs.We then approach some algebraic characterization problems concerning relationships between the BLMBPs under two diferent TGLMs.As applications,two specifc cases are presented to illustrate the main contributions in the study.
