Provider: ingentaconnect
Database: ingentaconnect
Content: application/x-research-info-systems
TY - ABST
AU - Gregoire, Timothy G.
AU - Lin, Qi Feng
AU - Boudreau, Johnathan
AU - Nelson, Ross
TI - Regression Estimation Following the Square-Root Transformation of the Response
JO - Forest Science
PY - 2008-10-01T00:00:00///
VL - 54
IS - 6
SP - 597
EP - 606
KW - nonlinearity
KW - back-transformation bias
N2 - In a variety of regression situations, there is interest in predicting the value of *Y* ^{2}, yet it is useful to model it using a square root transformation, such that *Y* rather than *Y* ^{2} is regressed on one or more covariates. The back-transformation bias of the square root transformation of the response variable of interest is presented in detail. An unbiased estimator is presented: *Ê*[*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2} + − *V*(_{ y|x∗} ^{2}). Its performance is compared against that of two biased estimators: *Ê*_{b} [*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2} + and *Ê*_{p} [*Y* ^{2}|*x* _{∗}] = _{ y|x∗} ^{2}. The first two moments of these estimators are derived analytically and verified by means of a simulation study. Both biased estimators have lower mean square errors than the unbiased estimator. An example wherein aboveground biomass is the response variable is presented for illustration.
UR - http://www.ingentaconnect.com/content/saf/fs/2008/00000054/00000006/art00004
ER -