TY - JOUR
T1 - A bayesian comparison of some estimators used in linear regression with multicollinear data
AU - Oman, Samuel D.
PY - 1978/1/1
Y1 - 1978/1/1
N2 - Several estimators (ridge, principal components, generalized inverse and Stein) have been proposed as alternatives to least squares for the multiple linear regression model when the independent variables are multicollinear. These methods differ in the way they adjust the least squares estimate to where the regression vector β “ought to be”. From a Bayesian point of view, they assume different prior distributions for β. In this paper t is expressed in such a way that the assumptions about the model which are implicit in a given prior distribution of jg become apparent. The Stein estimate can be viewed as assuming the independent variables to be “inherently multicollinear”, while the ridge estimate assumes they are not. Principal components and generalized inverse estimators correspond to a somewhat peculiar set of prior assumptions. A modification of the Stein estimate which is “smoother” than the principal components estimator is proposed.
AB - Several estimators (ridge, principal components, generalized inverse and Stein) have been proposed as alternatives to least squares for the multiple linear regression model when the independent variables are multicollinear. These methods differ in the way they adjust the least squares estimate to where the regression vector β “ought to be”. From a Bayesian point of view, they assume different prior distributions for β. In this paper t is expressed in such a way that the assumptions about the model which are implicit in a given prior distribution of jg become apparent. The Stein estimate can be viewed as assuming the independent variables to be “inherently multicollinear”, while the ridge estimate assumes they are not. Principal components and generalized inverse estimators correspond to a somewhat peculiar set of prior assumptions. A modification of the Stein estimate which is “smoother” than the principal components estimator is proposed.
KW - biased estimation
KW - principal components regression
KW - ridge regression
KW - shrinkage estimators
KW - Stein estimate
UR - http://www.scopus.com/inward/record.url?scp=4444255145&partnerID=8YFLogxK
U2 - 10.1080/03610927808827646
DO - 10.1080/03610927808827646
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AN - SCOPUS:4444255145
SN - 0361-0926
VL - 7
SP - 517
EP - 534
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 6
ER -