Stéphane Laurent

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PhD in theoretical probability. Author of a few papers in probability and statistics. Currently work as a statistical consultant.

	3,491 reputation	bio	website		visits	member for	1 year, 4 months
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May 4	comment	Conditional expectation of R-squared Just a thought before leaving you: the noncentral Chi² can be written as a mixture of (central) Chi² with a Poisson mixing distribution on the degrees of freedom. This should yield the 1st moment of the noncentral Beta without difficulty.
May 4	comment	Conditional expectation of R-squared Noncentral Fisher distributions as well as noncentral Beta distributions are defined from the noncentral Chi² distribution, similarly to the "central" case (noncentrality parameter $=0$).
May 4	comment	Conditional expectation of R-squared Type I, obviously: type II are distributed on $(0, \infty)$. Actually $R^2/(1-R^2)$ has the type II distribution. I have done the last corrections for today.
May 4	revised	Conditional expectation of R-squared deleted 4 characters in body
May 4	comment	Conditional expectation of R-squared I'm stupid ! The last equality of my answer if $\mu = \mu$ ! Sorry I'm tired.
May 4	comment	Conditional expectation of R-squared $\bar \mu = \frac{1}{n} \sum \mu_i$
May 4	comment	Conditional expectation of R-squared Done - do you see any simplification ?
May 4	revised	Conditional expectation of R-squared added 54 characters in body
May 4	revised	Conditional expectation of R-squared added 54 characters in body
May 4	comment	Conditional expectation of R-squared Beware of $Px \neq \Vert P x \Vert^2$. I'm going to edit my post to write the formulas.
May 4	comment	Conditional expectation of R-squared No, this is a linear projection. Your proposal are quadratic.
May 4	comment	Conditional expectation of R-squared Not really linear in $Y$ :)
May 4	comment	Conditional expectation of R-squared $P_Z x$ is the orthogoanl projection of $x$ on the linear subspace $Z$. And $P^\perp$ denotes projection on the orthogonal.
May 4	answered	Conditional expectation of R-squared
May 4	comment	Build statistical model @Andy I don't know. May be googling with the keyword "interval censored covariates" could give some hints.
May 4	comment	Conditional expectation of R-squared Oooppss sorry, my previous claim is true only under the hypothesis of the "null model" (intercept only). Otherwise the distribution of $R^2$ should be something like a noncentral Beta distribution, with a noncentrality parameter involving the unknown parameters.
May 4	comment	Conditional expectation of R-squared $R^2$ has a Beta distribution with parameters depending only on $n$ and $p$. No ?
May 4	comment	Build statistical model The solution surely depends on why you have interval data for the covariates.
May 4	comment	Variance of powers of a random variable @whuber In your first comment you seem to claim that distributions with arbitrary high moments are characterized by their moments, this is not true (considering integer powers only).
May 3	comment	Proof of relationship between hazard rate, probabilty density, survival function Have you noted that $h(t)$ is the derivative of $- \log S(t)$ ?