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15 janvier 2020
- doi: 10.58079/ovec
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Arthur Charpentier, « On Cochran Theorem (and Orthogonal Projections) », Freakonometrics, ID : 10.58079/ovec
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Cochran Theorem - from The distribution of quadratic forms in a normal system, with applications to the analysis of covariance published in 1934 - is probably the most import one in a regression course. It is an application of a nice result on quadratic forms of Gaussian vectors. More precisely, we can prove that if [latex]\boldsymbol{Y}\sim\mathcal{N}(\boldsymbol{0},\mathbb{I}_d)[/latex] is a random vector with [latex]d[/latex] [latex]\mathcal{N}(0,1)[/latex] variable then (i) if [latex]A[/...