vcm, vcx#

Purpose#

Computes an estimate of a variance-covariance matrix.

Format#

vc = vcm(m[, ddof])#

vc = vcx(x[, ddof])#

Parameters:

m (KxK moment (\(x'x\)) matrix) – A constant term MUST have been the first variable when the moment matrix was computed.
x (NxK matrix) – data
ddof (Scalar) – Optional input, delta degrees of freedom. The divisor will be \((N - ddof)\). Default = 1 (sample covariance matrix).

Returns:

vc (KxK variance-covariance matrix) – an estimate of the variance-covariance matrix.

Examples#

Compute covariance matrices from a data matrix, \(x\).

x = { 2 3,
      3 0,
      4 4,
      1 2 };

// Compute the sample covariance matrix
vcs = vcx(x);

// Compute the population covariance matrix
vcp = vcx(x, 0);

// Compute the sample covariance matrix
vcs2 = vcx(x, 1);

After the above code:

vcs  =  1.6666667       0.5000000
        0.5000000       2.9166667

vcp  =  1.2500000       0.3750000
        0.3750000       2.1875000

vcs2 =  1.6666667       0.5000000
        0.5000000       2.9166667

Compute covariance matrices from a moment matrix, \(x'x\).

// Create matrix with a constant
x = { 1 2 3,
      1 3 0,
      1 4 4,
      1 1 2 };

// Compute moment matrix
m = x'x;

// Compute the sample covariance matrix
vcs = vcm(m);

// Compute the population covariance matrix
vcp = vcm(m, 0);

// Compute the sample covariance matrix
vcs2 = vcm(m, 1);

After the above code:

vcs  =  1.6666667       0.5000000
        0.5000000       2.9166667

vcp  =  1.2500000       0.3750000
        0.3750000       2.1875000

vcs2 =  1.6666667       0.5000000
        0.5000000       2.9166667

Source#

corr.src