# 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.

sdr, subspaceDistance