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Results tagged with least-squares
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user 11697
Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.
11
votes
2
answers
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Gauss-Markov theorem: BLUE and OLS
I'm reading up on the Guass-Markov theorem on wikipedia, and I was hoping somebody could help me figure out the main point of the theorem.
We assume a linear model, in matrix form, is given by:
$$ y …
- 852
0
votes
Accepted
Gauss-Markov theorem: BLUE and OLS
It seems my hunch was correct indeed, as confirmed, e.g. on page 375 of the book
Introductory Econometrics. Relevant excerpt:
- 852
10
votes
1
answer
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Is the OLS estimator the UMVUE (assuming Normality)?
Suppose
$$
\mathbf{y} = \mathbf{X} \mathbf{b} + \mathbf{e} \, ,
\\
\mathbf{e} \sim \mathcal{N}(0,\mathbf{I}_P) \, .
$$
We know that $\mathbf{\hat{b}} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \m …
- 852