| cov_block_autocorrelation {sparsediscrim} | R Documentation |
Generates a p \times p block-diagonal covariance matrix with
autocorrelated blocks.
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
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:
\Sigma = \Sigma^{(\rho)} \oplus \Sigma^{(-\rho)} \oplus \ldots \oplus
\Sigma^{(\rho)},
where \oplus denotes the direct sum and the
(i,j)th entry of \Sigma^{(\rho)} is
\Sigma_{ij}^{(\rho)} =
\{ \rho^{|i - j|} \}.
The matrix \Sigma^{(\rho)} is the autocorrelated block discussed above.
The value of rho must be such that |\rho| < 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.
Value
autocorrelated covariance matrix