theoryRowpenUpperBound function

Penalty Parameter for Covariance Estimation Based on Theory

This function returns a theoretically-guided choice of the glasso penalty parameter, based on both the row and column covariance matrices.

theoryRowpenUpperBound(A, B, n1, n2)

Arguments

• A: column covariance matrix.
• B: row covariance matrix.
• n1: sample size of group one.
• n2: sample size of group two.

Returns

Returns a theoretically guided choice of the glasso penalty parameter.

Examples

# Define sample sizes
n1 <- 10
n2 <- 10
n <- n1 + n2
m <- 2e3
# Column covariance matrix (autoregressive of order 1)
A <- outer(1:n, 1:n, function(x, y) 0.2^abs(x - y))
# Row covariance matrix (autoregressive of order 1)
B <- outer(1:n, 1:n, function(x, y) 0.8^abs(x - y))
# Calculate theoretically guided Gemini penalty.
rowpen <- theoryRowpenUpperBound(A, B, n1, n2)
print(rowpen)

References

Joint mean and covariance estimation with unreplicated matrix-variate data Michael Hornstein, Roger Fan, Kerby Shedden, Shuheng Zhou (2018). Joint mean and covariance estimation with unreplicated matrix-variate data. Journal of the American Statistical Association