GeminiBPath function

Estimate Row-Row Covariance Using Gemini for a Sequence of Penalties

GeminiBPath estimates the row-row covariance, inverse covariance, correlation, and inverse correlation matrices using Gemini with a sequence of penalty parameters. For identifiability, the covariance factors A and B are scaled so that A has trace m, where m is the number of columns of X, A is the column-column covariance matrix, and B is the row-row covariance matrix.

GeminiBPath(X, rowpen.list, penalize.diagonal = FALSE)

Arguments

• X: Data matrix, of dimensions n by m.

• rowpen.list: Vector of penalty parameters, should be increasing (analogous to the glassopath

  function of the glasso package).

• penalize.diagonal: Logical indicating whether to penalize the off-diagonal entries of the correlation matrix. Default is FALSE.

Returns

• corr.B.hat: array of estimated correlation matrices, of dimension (nrow(X), nrow(X), length(rowpen.list)).

• corr.B.hat.inv: array of estimated inverse correlation matrices, of dimension (nrow(X), nrow(X), length(rowpen.list)).

• B.hat: array of estimated covariance matrices, of dimension (nrow(X), nrow(X), length(rowpen.list)).

• B.hat.inv: array of estimated inverse covariance matrices, of dimension (nrow(X), nrow(X), length(rowpen.list)).

Examples

# Generate a data matrix.
n1 <- 5
n2 <- 5
n <- n1 + n2
m <- 20
X <- matrix(rnorm(n * m), nrow=n, ncol=m)

# Apply GeminiBPath for a sequence of penalty parameters.
rowpen.list <- sqrt(log(m) / n) * c(1, 0.5, 0.1)
out <- GeminiBPath(X, rowpen.list, penalize.diagonal=FALSE)

# Display the estimated correlation matrix corresponding
# to penalty 0.1, rounded to two decimal places.
print(round(out$corr.B.hat[, , 3], 2))