If rows of $X$ are i.i.d $N_p(0,1)$ ,how to prove that $tr(X'X)$ is independent of any scale invariant function of $X$ ?
Including having no idea of where to start with, I have one more doubt: What s exactly meant by scale-invariant function?
$tr(X'X)$ is independent of any scale invariant function of $X$
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0What is $N_{p}(0,1)$? Standard normal? In fact I am confused about dimensions/objects here. – 2017-02-07
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0@Jan Yes , $N_p(0,I)$ refers to standard multivariate $p-$normal with dispersion matrix $\Sigma$ – 2017-02-07
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0And $X$ is $p$ vector so that $X'X$ is a number? If $X$ is $1\times p$, then $X'X$ is variance-covariance matrix, well expectation of its version (without subtracting first moments). What am I missing? – 2017-02-07
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0@Jan $X$ by default is a column vector. – 2017-02-07
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1Scale invariant means rotation by an orthogonal matrix. Now it should be simple. – 2017-02-13
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0@LandonCarter You could as well have posted this line in the below section.. One of the most precise hints I have got.. Thanks.. – 2017-02-15
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0@Qwerty Wizened men seldom go for upvotes :) – 2017-02-16