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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.

62J02General nonlinear regression
62J99Linear statistical inference
62F12Asymptotic properties of parametric estimators
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