Specifying a Prior Distribution in Structured Regression Problems

Abstract The problem of assessing the prior mean and covariance matrix of the vector of regression coefficients in the normal multiple linear regression model is considered. Arguments are advanced for using expectations regarding the form of the design matrix in specifying the prior for problems with a structure that can aid in specifying these expectations. This is illustrated with models having second-order terms. An example is given.

[1]  Arnold Zellner,et al.  Applications of Bayesian Analysis in Econometrics , 1983 .

[2]  Samuel D. Oman,et al.  Shrinking Towards Subspaces in Multiple Linear Regression , 1982 .

[3]  Edward Leamer.  Coordinate-Free Ridge Regression Bounds , 1981 .

[4]  Wayne S. Smith,et al.  Interactive Elicitation of Opinion for a Normal Linear Model , 1980 .

[5]  Gary Smith,et al.  A Critique of Some Ridge Regression Methods , 1980 .

[6]  Robert L. Mason,et al.  Some Considerations in the Evaluation of Alternate Prediction Equations , 1979 .

[7]  A. Dempster.  Conditional Confidence Statements and Confidence Estimators: Comment , 1977 .

[8]  A. F. Smith.  A Simulation Study of Alternatives to Ordinary Least Squares: Comment , 1977 .

[9]  B. Efron,et al.  A Simulation Study of Alternatives to Ordinary Least Squares: Comment , 1977 .

[10]  Edward E. Leamer,et al.  Matrix Weighted Averages and Posterior Bounds , 1976 .

[11]  R. Snee,et al.  Ridge Regression in Practice , 1975 .

[12]  C. Theobald.  Generalizations of Mean Square Error Applied to Ridge Regression , 1974 .

[13]  A. F. Smith,et al.  Ridge-Type Estimators for Regression Analysis , 1974 .

[14]  B. Efron,et al.  Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach , 1973 .

[15]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[16]  Donald W. Marquaridt.  Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[17]  Stanley L. Sclove,et al.  Improved Estimators for Coefficients in Linear Regression , 1968 .

[18]  G. C. Tiao,et al.  Bayes's theorem and the use of prior knowledge in regression analysis , 1964 .

[19]  Howard Raiffa,et al.  Applied Statistical Decision Theory. , 1961 .