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Biometrika 1998 85(3):749-754; doi:10.1093/biomet/85.3.749
© 1998 by Biometrika Trust
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MISCELLANEA

A note on transforming a response variable for linearity

PEIDE SHI and WING-KAM FUNG

Department of Probability and Statistics, Peking University Beijing 100871, P.R. Chinapdshi{at}statms.stat.pku.edu.cn
Department of Statistics, The University of Hong Kong Pokfulam Road, Hong Konghrntfwk{at}hkucc.hku.hk

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)|x}, 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 similar but in some applications Cook & Weisberg's estimate may be improved by further iterations of the procedure.

Key Words: B-spline • Box-Cox transformation • Canonical correlation • Nonparametric regression.


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