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Math Help - Simultaneous confidence interval and constrasts

  1. #1
    Moo
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    Simultaneous confidence interval and constrasts

    Hi guys !

    I have a quick question :
    We don't understand why it is better to consider contrasts (linear combination of parameters (\beta_j)_{j\in J} : \sum_{j=1}^J c_j \beta_j, where \sum_{j=1}^J c_j =0) in the Scheffé method for simultaneous confidence intervals...
    Why do we need the latter sum to be 0 ? I read in a lecture note that if we consider contrasts instead of any linear combination, we're considering a Fisher distribution with a degree of freedom that is J-1 instead of J. But is it really the only reason ?

    Thanks for any input, even if it doesn't exactly answer the question... if it casts a light on some point of the Scheffé method, I would also be pleased
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  2. #2
    MHF Contributor matheagle's Avatar
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    I believe it has to do with the column space of your design matrix
    https://netfiles.uiuc.edu/dgs/www/st...tes/042804.pdf
    I used to teach that, but it's been a few years.
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  3. #3
    Moo
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    Well, sorry, I didn't really find the answer in this paper... I'm quite abstruse to algebra, so I don't understand the thing with column space :s

    Thanks anyway
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