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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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