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@anchor{doc-gls}
- Function File: [beta, v, r] = gls (y, x, o)
-
Generalized least squares estimation for the multivariate model
y = x b + e with mean (e) = 0 and
cov (vec (e)) = (s^2) o,
where
y is a t by p matrix, x is a t by
k matrix, b is a k by p matrix, e
is a t by p matrix, and o is a t p by
t p matrix.
Each row of y and x is an observation and each column a
variable. The return values beta, v, and r are
defined as follows.
- beta
-
The GLS estimator for b.
- v
-
The GLS estimator for s^2.
- r
-
The matrix of GLS residuals, r = y - x beta.
@anchor{doc-ols}
- Function File: [beta, sigma, r] = ols (y, x)
-
Ordinary least squares estimation for the multivariate model
y = x b + e with
mean (e) = 0 and cov (vec (e)) = kron (s, I).
where
y is a t by p matrix, x is a t by
k matrix, b is a k by p matrix, and
e is a t by p matrix.
Each row of y and x is an observation and each column a
variable.
The return values beta, sigma, and r are defined as
follows.
- beta
-
The OLS estimator for b,
beta = pinv (x) *
y
, where pinv (x)
denotes the pseudoinverse of
x.
- sigma
-
The OLS estimator for the matrix s,
sigma = (y-x*beta)'
* (y-x*beta)
/ (t-rank(x))
- r
-
The matrix of OLS residuals,
r = y - x *
beta
.
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