jointMeanCovGroupCen {jointMeanCov}

Estimate Mean and Row-Row Correlation Matrix Using Group Centering

Description

This function implements Algorithm 1 from Hornstein, Fan, Shedden, and Zhou (2018), doi: 10.1080/01621459.2018.1429275. Given an n by m data matrix, with a vector of indices denoting group membership,this function estimates the row-row inverse covariance matrix after a preliminary group centering step, then uses the estimated inverse covariance estimate to perform GLS mean estimation. The function also returns test statistics comparing the group means for each column, with standard errors accounting for row-row correlation.

Usage

jointMeanCovGroupCen(X, group.one.indices, rowpen, B.inv = NULL)

Arguments

X

Data matrix.

group.one.indices

Vector of indices denoting rows in group one.

rowpen

Glasso penalty for estimating B, the row correlation matrix.

B.inv

Optional row-row covariance matrix to be used in GLS. If this argument is passed, then it is used instead of estimating the inverse row-row covariance.

Value

B.hat.inv

Estimated row-row inverse covariance matrix. For identifiability, A and B are scaled so that A has trace m, where m is the number of columns of X.

corr.B.hat.inv

Estimated row-row inverse correlation matrix.

gls.group.means

Matrix with two rows and m columns, where m is the number of columns of X. Entry (i, j) contains the estimated mean of the jth column for an individual in group i, with i = 1,2, and j = 1, ..., m.

gamma.hat

Estimated group mean differences.

test.stats

Vector of test statistics of length m.

p.vals

Vector of two-sided p-values, calculated using the standard normal distribution.

p.vals.adjusted

Vector of p-values, adjusted using the Benjamini-Hochberg fdr adjustment.

Examples

# Define sample sizes
n1 <- 5
n2 <- 5
n <- n1 + n2
m <- 200

# Generate data with row and column covariance
# matrices each autorogressive of order one with
# parameter 0.2.  The mean is defined so the first
# three columns have true differences in group means
# equal to four.
Z <- matrix(rnorm(m * n), nrow=n, ncol=m)
A <- outer(1:m, 1:m, function(i, j) 0.2^abs(i - j))
B <- outer(1:n, 1:n, function(i, j) 0.2^abs(i - j))
M <- matrix(0, nrow=nrow(Z), ncol=ncol(Z))
group.one.indices <- 1:5
group.two.indices <- 6:10
M[group.one.indices, 1:3] <- 2
M[group.two.indices, 1:3] <- -2
X <- t(chol(B)) %*% Z %*% chol(A) + M

# Apply Algorithm 1 (jointMeanCovGroupCen) and
# plot the test statistics.
rowpen <- sqrt(log(m) / n)
out <- jointMeanCovGroupCen(X, group.one.indices, rowpen)
plot(out)
summary(out)