Given the kernel matrix that characterises a central subspace, this function estimates the dimension of the subspace.
dimhat(M)Kernel of subspace. A symmetric, non-negative definite, numeric
matrix, typically obtained from sdr.
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.