spatstat.core (version 2.2-0)

dimhat: Estimate Dimension of Central Subspace

Description

Given the kernel matrix that characterises a central subspace, this function estimates the dimension of the subspace.

Usage

dimhat(M)

Arguments

M

Kernel of subspace. A symmetric, non-negative definite, numeric matrix, typically obtained from sdr.

Value

A single integer giving the estimated dimension.

Details

This function computes the maximum descent estimate of the dimension of the central subspace with a given kernel matrix M.

The matrix M should be the kernel matrix of a central subspace, which can be obtained from sdr. It must be a symmetric, non-negative-definite, numeric matrix.

The algorithm finds the eigenvalues ${\lambda }_1\ge \dots \ge {\lambda }_n$ of $M$, and then determines the index $k$ for which ${\lambda }_k/{\lambda }_{k-1}$ is greatest.

References

Guan, Y. and Wang, H. (2010) Sufficient dimension reduction for spatial point processes directed by Gaussian random fields. Journal of the Royal Statistical Society, Series B, 72, 367--387.

See Also

sdr, subspaceDistance