Generalization of the geometric mean functional relationship Export

@article{citeulike:5073144, abstract = {The measurement error model for multi-variable planar regression of Y on X 1 , X 2 ,…, and X k 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.}, author = {Draper, N.}, citeulike-article-id = {5073144}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0167-9473(96)00037-0}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0167-9473(96)00037-0}, day = {09}, doi = {10.1016/S0167-9473(96)00037-0}, issn = {01679473}, journal = {Computational Statistics \& Data Analysis}, keywords = {algorithm, optimization, total-least-squares}, month = {January}, number = {3}, pages = {355--372}, posted-at = {2009-07-06 10:04:02}, priority = {2}, title = {Generalization of the geometric mean functional relationship}, url = {http://dx.doi.org/10.1016/S0167-9473(96)00037-0}, volume = {23}, year = {1997} }

TY - JOUR ID - citeulike:5073144 L3 - citeulike-article-id:5073144 N2 - The measurement error model for multi-variable planar regression of Y on X 1 , X 2 ,…, and X k 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. IS - 3 JF - Computational Statistics & Data Analysis SN - 01679473 EP - 372 TI - Generalization of the geometric mean functional relationship VL - 23 SP - 355 KW - algorithm KW - optimization KW - total-least-squares AU - Draper, N PY - 1997/01/09/ UR - http://dx.doi.org/10.1016/S0167-9473(96)00037-0 ER -