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
Feb
9
comment Left justifying in \genfrac
Wow -- thanks for the extensive explanation!
Feb
8
comment Left justifying in \genfrac
Thanks, this seems to work! I accept the answer, but idly wonder why \hfill provides the desired behavior...
Feb
8
accepted Left justifying in \genfrac
Feb
8
asked Left justifying in \genfrac
Jan
27
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
@Strants This problem came from my analysis of the properties of estimators for the parameters of log-normal distributions under certain constraints on the observations (induced by the post-processing requirements). It actually turns out that there was a mistake in my analysis, so the expression developed here is not very relevant to me anymore. However, I like that I learned a neat new interpretation for hyperbolic cosine by asking this question...
Jan
27
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Came back to this a few days later and now it's clear to me what you did--it is indeed very clever! Thanks!
Jan
27
accepted An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Jan
23
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
@sciona Well, if you are correct, then $A_{f(n)}(n)=\operatorname{cosh}^n f(n)$. In fact, I am certain that you are correct, but I still can't wrap my mind around your last equality. But that could be because I'm quite tired...
Jan
23
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
I'm not sure how you obtain the second equality. In fact, $(e^{f(n)}+e^{-f(n)})^n\geq e^{nf(n)}\geq A_{f(n)}(n)$, with the second equality holding only when $f(n)=0$...
Jan
22
asked An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Jan
16
comment Does bounding moments make distributions close in total variation distance?
Great point -- this completely makes sense. Now I wonder what are these other conditions on the distributions in $\mathcal{W}$ that would result in the total variation distance bound. Obviously, if $\mathcal{W}$ contains a set of slightly disturbed $W$'s, the bound should trivially hold. I wonder if the set is larger...
Jan
16
asked Does bounding moments make distributions close in total variation distance?
Dec
19
comment A reference for Pearson's chi-squared testing
I have considered Pearson's original paper, but decided against it based on item (ii) in @Glen_b's comment. The dearth of references to the literature describing a chi-squared test is rather surprising that, considering that there is a myriad of chi-squared testing tutorials on the web. I am not a statistician, but is it something considered "common knowledge" in the stats community? (like you don't reference calculus books when claiming that the first derivative of location is the velocity)
Dec
19
asked A reference for Pearson's chi-squared testing
Dec
15
accepted Trace distance between "weighted" Hermitian matrices
Dec
15
asked Trace distance between "weighted" Hermitian matrices
Nov
28
accepted How many ways can one "fit" $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$?
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