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Results tagged with mathematical-statistics
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user 49404
Mathematical theory of statistics, concerned with formal definitions and general results.
1
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Is the joint distribution of two linear combinations of Gaussians still a multivariate normal?
Suppose I have $\textbf{X}$ ~ $N(\textbf{0},\Sigma)$, and I'm considering two different linear combinations, $a^* X$ and $b^* X$, which we suppose are uncorrelated. I understand that linear combinatio …
- 467
1
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0
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Is there a geometric interpretation for the surprising result of $E[x(y-\mu_y)] = COV(x,y)$?
I was playing around with non-central second moments, and noticed that $E[x(y-\mu_y)] = E[(x-\mu_x + \mu_x)(y-\mu_y)] = COV[x,y] + E[\mu_x(y-\mu_y) = COV[x,y] + 0$.
I find this very surprising. It ap …
- 467
7
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1
answer
207
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How is it possible for both the likelihood and log-likelihood to be asymptotically normal?
I was trying to understand asymptotic normality of the posterior better, and came across a confusing point. So let's say we have a likelihood, $$L(\theta | X) = \prod_{i=1}^n p(X_i | \theta), $$ so th …
- 467