R: Estimate Dimension of Central Subspace

dimhat {spatstat.core} | R Documentation

## 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`.

### 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] ≥ ...≥ 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.

### Author(s)

Matlab original by Yongtao Guan, translated to R by Suman Rakshit.

### 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`

[Package spatstat.core version 1.65-5 Index]