Asymptotics of sliced inverse regression
Asymptotics of sliced inverse regression
Sliced Inverse Regression is a method for reducing the dimension of the explanatory variables x in non-parametric regression problems. Li (1991) discussed a version of this method which begins with a partition of the range of y into slices so that the conditional covariance matrix of x given y can be estimated by the sample covariance matrix within each slice. After that the mean of the conditional covariance matrix is estimated by averaging the sample covariance matrices over all slices. Hsing and Carroll (1992) have derived the asymptotic properties of this procedure for the special case where each slice contains only two observations. In this paper we consider the case that each slice contains an arbitrary but fixed number of yi and more generally the case when the number of yi per slice goes to infinity. The asymptotic properties of the associated eigenvalues and eigenvectors are also obtained.
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- University of Hong Kong China (People's Republic of)
- University of Hong Kong (香港大學) China (People's Republic of)
519, eigenvalues and eigenvectors, conditional covariance matrix, Density estimation, Linear inference, regression, sample covariance matrix, dimension reduction, nonparametric regression, Asymptotic properties of nonparametric inference, eigenvalues, eigenvectors, sliced inverse regression, Asymptotics
519, eigenvalues and eigenvectors, conditional covariance matrix, Density estimation, Linear inference, regression, sample covariance matrix, dimension reduction, nonparametric regression, Asymptotic properties of nonparametric inference, eigenvalues, eigenvectors, sliced inverse regression, Asymptotics
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