PlotNormTest (version 1.0.1)

covZtZs: Covariance matrix of derivatives of sample moment generating function (MGF).

Description

Stacking derivatives upto the third/fourth orders of sample MGF together to obtain a vector, which (under normality assumption) approaches a multivariate normally distributed vector with zero mean and a covariance matrix. covZtZs calculates covariance between any two points \(t\) and \(s\) in \(\mathbb{R}^p\).

Usage

mt3_covZtZs(t, s, pos.matrix = NULL)
mt4_covZtZs(t, s, pos.matrix = NULL)

Value

mt3_covZtZs Covariance matrix relating to the use of third derivatives.

mt4_covZtZs Covariance matrix relating to the use of fourth derivatives. This also contains information on the third third derivatives mt3_covZtZs.

Arguments

t, s

a vector of length \(p\).

pos.matrix

matrix contains information of positions of derivatives. Default is NULL, where the function will call mt3_pos() or mt4_pos().

Examples

set.seed(1)
p <- 3
x <- MASS::mvrnorm(100, rep(0, p), diag(p))
t <- rep(0.2, p)
s <- rep(-.3, p)
# Using third derivatives
pos.matrix3 <- mt3_pos(p)
sZtZs3 <- mt3_covZtZs(t, s, pos.matrix = pos.matrix3)
dim(sZtZs3)
sZtZs3[1:5, 1:5]
# Using fourth derivatives
sZtZs4 <- mt4_covZtZs(t, s)
dim(sZtZs4)
sZtZs4[1:5, 1:5]