Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary γ under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.
Bibliographical noteFunding Information:
The authors would like to thank the editor, an associate editor and one anonymous referee for their constructive comments. This research was supported by the National Science Foundation, U.S.A.
- Central subspace
- Continuum regression
- Ordinary least squares
- Partial least squares
- Principal components
- Sufficient dimension reduction