R/SPU_Var_diffcov.R

In highmean: Two-Sample Tests for High-Dimensional Mean Vectors

SPU_Var_diffcov <- function(gamma, n1, n2, cov1, cov2){
	p <- dim(cov1)[1]
	if(gamma == 1){
		var <- sum(cov1)/n1 + sum(cov2)/n2
	}else{
		P1 <- SPU_E_diffcov(2*gamma, n1, n2, cov1, cov2)
		P2 <- -(SPU_E_diffcov(gamma, n1, n2, cov1, cov2))^2
		c_d <- c_and_d(gamma, gamma)
		n.case <- dim(c_d)[1]
		P3 <- 0
		diags1 <- diag(cov1)
		mat1.col <- matrix(rep(diags1, p), p, p, byrow = FALSE)
		mat1.row <- matrix(rep(diags1, p), p, p, byrow = TRUE)
		diags2 <- diag(cov2)
		mat2.col <- matrix(rep(diags2, p), p, p, byrow = FALSE)
		mat2.row <- matrix(rep(diags2, p), p, p, byrow = TRUE)
		for(i in 1:n.case){
			c1 <- c_d$c1[i]
			c2 <- c_d$c2[i]
			c3 <- c_d$c3[i]
			d1 <- c_d$d1[i]
			d2 <- c_d$d2[i]
			d3 <- c_d$d3[i]
			mat <- mat1.col^c1*mat1.row^c2*cov1^c3*mat2.col^d1*mat2.row^d2*cov2^d3
			diag(mat) <- 0
			N <- (factorial(gamma))^2*sum(mat)
			D <- (n1^(c1 + c2 + c3)*n2^(d1 + d2 + d3)*factorial(c1)*factorial(c2)*factorial(d1)*factorial(d2)*factorial(c3)*factorial(d3)*2^(c1 + c2 + d1 + d2))
			P3 <- P3 + N/D
		}
		var <- P1 + P2 + P3
	}
	return(var)
}