Generalization of the geometric mean functional relationship

Abstract The measurement error model for multi-variable planar regression of Y on X1,X2,…, and Xk is reconsidered. A measure of the dispersion of a point from a fitted plane is used to construct a new measure of deviation for regression. Minimizing this provides estimates of the model parameters. The relationships of these estimates to those obtained from the k + 1 ordinary least-square (OLS) estimates which use X's and Y as response variables is investigated. The estimates from minimizing the new deviation can be shown to be a convex combination of the k + 1 OLS regression estimates. For k = 1, the geometric mean functional relationship is obtained.