Given the kernel matrix that characterises a central subspace, this function estimates the dimension of the subspace.
dimhat(M)A single integer giving the estimated dimension.
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.
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.
sdr, subspaceDistance