2d
accepted Distribution of an angle between a random and fixed unit-length $n$-vectors
2d
comment Distribution of an angle between a random and fixed unit-length $n$-vectors
Thanks for a great explanation! One note: the coefficient simplifies to $\frac{\Gamma(\frac{n}{2})}{\sqrt{\pi}\Gamma(\frac{n-1}{2})}$ using the property that defines the Gamma function $\Gamma(t+1)=t\Gamma(t)$.
2d
revised Distribution of an angle between a random and fixed unit-length $n$-vectors
addressed comment
2d
comment Distribution of an angle between a random and fixed unit-length $n$-vectors
Thanks for the explanation -- but how does it apply to $n$ sphere? The volume element looks a lot more complicated -- does one just integrate out the other dimensions? And yes, I overlooked the fact that the angle between vectors cannot exceed $\pi$ (will fix the question).
Apr
23
comment Eliminating a nuisance parameter in likelihood ratio test
@Xi'an As I mentioned earlier, van Trees also seconds this.
Apr
23
comment Eliminating a nuisance parameter in likelihood ratio test
@Glen_b I changed the question per your suggestion. Sorry for the lack of clarity.
Apr
23
revised Eliminating a nuisance parameter in likelihood ratio test
changes per Glen_b's comments
Apr
23
comment Eliminating a nuisance parameter in likelihood ratio test
$\theta\in\{\theta_0,\theta_1\}$ is fixed but unknown, $\eta$ is random, and "uninteresting." Looks like van Trees has it the my co-author's way, Eq. (296) in Sec 2.5 "Composite Hypotheses"...
Apr
23
asked Eliminating a nuisance parameter in likelihood ratio test
Apr
22
asked Distribution of an angle between a random and fixed unit-length $n$-vectors
Apr
1
awarded Popular Question
Mar
31
comment Converse for Levy's continuity theorem
Ok, yes, that makes complete sense. Thanks for the example and clarification. I think I might be able to show an almost-sure convergence of the normalized max to Weibull in my problem, but that doesn't help me with convergence in $L^k$, which seems to be the only way to ensure moments converge...
Mar
31
revised Converse for Levy's continuity theorem
Fix typo in Weibull CDF
Mar
31
comment Converse for Levy's continuity theorem
I see, but now I am confused. The CF for Weibull is $\sum_{n=0}^\infty \frac{(it)^n}{n!}\Gamma(1+n/\alpha)$, obviously differentiable at $t=0$, however, it somehow doesn't seem right that the moments of (normalized) max converge to the moments of Weibull. Can anyone comment? (I can rephrase the question, or write a new question)
Mar
31
asked Converse for Levy's continuity theorem
Mar
26
accepted Integral involving $\operatorname{sinc}$ and exponential
Mar
25
asked Integral involving $\operatorname{sinc}$ and exponential
Feb
24
accepted Inequality involving absolute moment and variance
Feb
24
comment Inequality involving absolute moment and variance
Ahh, yes, that makes sense. And, by the same argument, for any $0<a\leq b$, $E[|X|^a]^{1/a}\leq E[|X|^b]^{1/b}$, so $f$ doesn't matter in my case.
Feb
24
asked Inequality involving absolute moment and variance
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