Sum_of_Wishart_df: The approximate degrees of freedom formula for sum of Wishart.

Description

The approximate degrees of freedom formula for sum of two independent Wishart random variable with parameter sig1 and sig2, and degrees of freedom n1-1 and n2-1 where n1 + n2 is equal to the total_sample_size.

See Koner and Luo (2023) for more details on the formula for degrees of freedom.

Usage

Sum_of_Wishart_df(total_sample_size, alloc.ratio, sig1, sig2)

Value

The approximate degrees of freedom.

Arguments

total_sample_size: Target sample size, must be a positive integer.
alloc.ratio: Allocation of total sample size into the two groups. Must set as a vector of two positive numbers. For equal allocation it should be put as c(1,1), for non-equal allocation one can put c(2,1) or c(3,1) etc.
sig1: The true (or estimate) of covariance matrix for the first group. Must be symmetric (is.symmetric(sig1) == TRUE) and positive definite (chol(sig1) without an error!).
sig2: The true (or estimate) of covariance matrix for the second group. Must be symmetric (is.symmetric(sig2) == TRUE) and positive definite (chol(sig2) without an error!).

Author

Salil Koner
Maintainer: Salil Koner salil.koner@duke.edu

Examples

Run this code


k <- 8
mu1  <- rep(0,k); del  <- 0.4; mu2 <- mu1 + rep(del, k);
sig1 <- diag(k); sig2 <- sig1 + del*toeplitz(c(1,rep(0.5, k-1)))
alt.dist.samples <- Sum_of_Wishart_df(total_sample_size=150,
sig1=sig1, sig2=sig2, alloc.ratio=c(2,1))