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Binary regressors in dimension reduction models: A new look at treatment comparisons. (English) Zbl 0828.62033
Summary: New aspects of treatment comparison are brought out via the dimension reduction model of the second author [J. Am. Stat. Assoc. 86, No. 414, 316-342 (1991; Zbl 0742.62044)] for general regression settings. Denoting the treatment indicator by $$Z$$ and the covariate by $$X$$, the model $$Y = g(v'X + \theta Z, \varepsilon)$$ is discussed in detail. Estimates of $$v$$ and $$\theta$$ 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 $$\theta$$. Asymptotic theory and a simulation study are presented.

##### MSC:
 62G07 Density estimation 62J02 General nonlinear regression
LISP-STAT