A note on transforming a response variable for linearity

Abstract

For the problem of choosing a transformation h(y) of a univariate response variable y to achieve the linearity of the regression function E{h(y)1x}, we view Cook & Weisberg's (1994) method as an iterative procedure and estimate the transformed linear model based on the fixed point of the iteration procedure. When the procedure is implemented with B-spline smoothing by projecting the function h(y) into a B-spline space, it is proved that the fixed point is identical to the solution obtained from the canonical correlation method proposed by He & Shen (1997). Real and simulated examples show that the results of Cook & Weisberg's and He & Shen's methods are often imilar but in some applications Cook & Weisberg's estimate may be improved by further iterations of the procedure.