dimhat

0th

Percentile

Estimate Dimension of Central Subspace

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

Keywords
multivariate, algebra, array
Usage
dimhat(M)
Arguments
M

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

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 \(\lambda_1 \ge \ldots \ge \lambda_n\) of \(M\), and then determines the index \(k\) for which \(\lambda_k/\lambda_{k-1}\) is greatest.

Value

A single integer giving the estimated dimension.

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

Aliases
  • dimhat
Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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