Maximum Likelihood Estimation for Sigma

This function obtains the MLE of Sigma covariance matrix for a multivariate normal population. The result is the biased estimator for Sigma because the denominator is \(n\).

mle_sigma(x, mu = NULL)

Arguments

x	a data frame.
mu	the vector with the mean if known.

Examples

# This example consider the dataset from example 5.2 From Johnson and Wichern (2007)
x1 <- c(3.7, 5.7, 3.8, 3.2, 3.1, 4.6, 2.4, 7.2, 6.7, 5.4, 3.9,
        4.5, 3.5, 4.5, 1.5, 8.5, 4.5, 6.5, 4.1, 5.5)
x2 <- c(48.5, 65.1, 47.2, 53.2, 55.5, 36.1, 24.8, 33.1, 47.4, 54.1,
        36.9, 58.8, 27.8, 40.2, 13.5, 56.4, 71.6, 52.8, 44.1, 40.9)
x3 <- c(9.3, 8, 10.9, 12, 9.7, 7.9, 14, 7.6, 8.5, 11.3, 12.7, 12.3,
        9.8, 8.4, 10.1, 7.1, 8.2, 10.9, 11.2, 9.4)
dt <- data.frame(x1, x2, x3)

# Estimating Sigma assuming unknow mu mean vector
mle_sigma(x=dt)
#>         x1       x2        x3
#> x1  2.7354   9.5095 -1.718600
#> x2  9.5095 189.7990 -5.358000
#> x3 -1.7186  -5.3580  3.446275

# Estimating Sigma assuming known mu mean vector
mle_sigma(x=dt, mu=c(4, 50, 10))
#>         x1       x2      x3
#> x1  3.1450   6.5655 -1.7410
#> x2  6.5655 210.9590 -5.1970
#> x3 -1.7410  -5.1970  3.4475