# cov_block_autocorrelation: Generates a p-dimensional block-diagonal covariance matrix... In sortinghat: sortinghat

## Description

This function generates a p \times p covariance matrix with autocorrelated blocks. The autocorrelation parameter is rho. There are num_blocks blocks each with size, block_size. The variance, sigma2, is constant for each feature and defaulted to 1.

## Usage

 1 2  cov_block_autocorrelation(num_blocks, block_size, rho, sigma2 = 1) 

## Arguments

 num_blocks the number of blocks in the covariance matrix block_size the size of each square block within the covariance matrix rho the autocorrelation parameter. Must be less than 1 in absolute value. sigma2 the variance of each feature

## Details

The autocorrelated covariance matrix is defined as:

Σ = Σ^{(ρ)} \oplus Σ^{(-ρ)} \oplus … \oplus Σ^{(ρ)},

where \oplus denotes the direct sum and the (i,j)th entry of Σ^{(ρ)} is

Σ_{ij}^{(ρ)} = \{ ρ^{|i - j|} \}.

The matrix Σ^{(ρ)} is the autocorrelated block discussed above.

The value of rho must be such that |ρ| < 1 to ensure that the covariance matrix is positive definite.

The size of the resulting matrix is p \times p, where p = num_blocks * block_size.

The block-diagonal covariance matrix with autocorrelated blocks was popularized by Guo et al. (2007) for studying classification of high-dimensional data.

## Value

autocorrelated covariance matrix

## References

Guo, Y., Hastie, T., & Tibshirani, R. (2007). "Regularized linear discriminant analysis and its application in microarrays," Biostatistics, 8, 1, 86-100.

sortinghat documentation built on May 30, 2017, 4:52 a.m.