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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
Software:
LISP-STAT
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