Abstract: In this paper, new aspects of treatment comparison are brought out via the dimension reduction model of Li (1991) for general regression settings. Denoting the treatment indicator by Z and the covariate by X, the model Y=g(v'x+θZ,ε) is discussed in detail. Estimates of v and θ are obtained without assuming a functional form for g. Our method is based on the use of SIR (sliced inverse regression) for reducing the dimensionality of the covariate, followed by a partial-inverse mean matching method for estimating the treatment effect θ. Asymptotic theory and a simulation study are presented.
Key words and phrases: Conditioning, dimension reduction, linear design condition, nonparametric curve fitting, randomization, SIR, treatment effect.