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24. Optimization

24.1 Linear Programming  
24.2 Quadratic Programming  
24.3 Nonlinear Programming  
24.4 Linear Least Squares  


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24.1 Linear Programming


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24.2 Quadratic Programming


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24.3 Nonlinear Programming


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24.4 Linear Least Squares

Function File: [beta, v, r] = gls (y, x, o)
Generalized least squares estimation for the multivariate model with and , where is a by matrix, is a by matrix, is a by matrix, is a by matrix, and is a by 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 .

v
The GLS estimator for .

r
The matrix of GLS residuals, .

Function File: [beta, sigma, r] = ols (y, x)
Ordinary least squares estimation for the multivariate model with and . where is a by matrix, is a by matrix, is a by matrix, and is a by 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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