theoryRowpenUpperBoundDiagA function

Penalty Parameter for Covariance Estimation Based on Theory

This function returns a theoretically-guided choice of the glasso penalty parameter, treating the column correlation matrix as the identity.

theoryRowpenUpperBoundDiagA(B, n1, n2, m)

Arguments

• B: row covariance matrix.
• n1: sample size of group one.
• n2: sample size of group two.
• m: number of columns of the data matrix (where the data matrix is of size n by m, with n = n1 + n2).

Returns

Returns a theoretically guided choice of the glasso penalty parameter.

Examples

# Define sample sizes
n1 <- 10
n2 <- 10
n <- n1 + n2
m <- 2e3
# 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 <- theoryRowpenUpperBoundDiagA(B, n1, n2, m)
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