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Slicing regression: A link-free regression method. (English) Zbl 0738.62070
For a general regression model of the form $$y=g(\alpha+x'\beta,\epsilon)$$ with an arbitrary and unknown link function $$g$$, the authors study the slicing regression for estimating the direction of $$\beta$$. They first estimate the inverse regression curve $$\epsilon(x\mid y)$$ using a step function and then estimate the covariance matrix $$\Gamma=\hbox{Cov } E(x\mid y)$$ using the estimated inverse regression curve. Finally, the spectral decomposition of the estimate $$\hat\Gamma$$ with respect to the sample covariance matrix of $$x$$ gives the principal eigenvector, which is the slicing regression estimate for the direction of $$\beta$$. The basic asymptotic theory for the slicing regression is established.

##### MSC:
 62J02 General nonlinear regression 62J99 Linear inference, regression 62F12 Asymptotic properties of parametric estimators
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