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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(α+x ' β,ϵ) with an arbitrary and unknown link function g, the authors study the slicing regression for estimating the direction of β. They first estimate the inverse regression curve ϵ(xy) using a step function and then estimate the covariance matrix Γ=CovE(xy) using the estimated inverse regression curve. Finally, the spectral decomposition of the estimate Γ ^ with respect to the sample covariance matrix of x gives the principal eigenvector, which is the slicing regression estimate for the direction of β. The basic asymptotic theory for the slicing regression is established.

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