151 reputation
7
bio website
location
age
visits member for 1 year, 5 months
seen Aug 13 at 20:47

Jan
2
comment 95% confidence interval around sum of random variables
@heropup If I'm estimating $\text{E}[X]$ using $\bar{X}$, as the mean of normal random variables, then I have a sample variance $S^2_X$. Do I have to divide this sample variance by $N^2$ before sticking it into the $\sqrt{a^2 \text{Var}[X] + b^2 \text{Var}[Y]}$ term to get the standard error for $W$? I'm always confused about when I have to divide a sample variance by $N^2$ to get the standard error.
Jan
2
comment 95% confidence interval around sum of random variables
@heropup Right, yes, that makes sense. I just wanted to clarify, to make sure I wasn't utterly confused :)
Jan
2
comment 95% confidence interval around sum of random variables
@heropup Just to clarify, generally speaking, the CI around $W$ would be $\text{E}[W] \pm z \cdot \text{SE}_W$, where SE is the standard error as you have written, and where $z$ is an appropriate test statistic. Is this correct?
Jan
2
accepted Estimate the number of integral solutions inside a convex polyhedron
Jan
2
comment 95% confidence interval around sum of random variables
@heropup But what do you mean by straightforward? There isn't any correlation, by the way, in the case I'm referring to. Are you simply saying that I can compute the lower and upper bounds of the CIs for $X$ and $Y$, and then plug those into the equation above and directly compute lower and upper bounds for $W$?
Jan
2
asked 95% confidence interval around sum of random variables
Jan
1
comment Notation for vector composed of subset of elements of another vector
@user18921 I see, thanks. What is the meaning of the symbol $\bigoplus$ in $\mathbb{R}^N \mapsto \bigoplus_{i=1}^N \mathbb{R}^i$? I realize it wasn't you who suggested this notation, but could you explain what it means in this context?
Dec
31
awarded  Tumbleweed
Dec
30
comment Notation for vector composed of subset of elements of another vector
I accepted @JoshChen 's answer because in an engineering context (in which this arose for me), the mathematical sophistication here is certainly more than is necessary. Nevertheless, I'm quite interested in understanding this answer (I'm an engineer, not a mathematician, so perhaps I'm a little slower than most participants in this discussion).
Dec
30
accepted Notation for vector composed of subset of elements of another vector
Dec
30
comment Notation for vector composed of subset of elements of another vector
@user18921 Question: what are the meanings of: the "ord" in Definition 0; and the open dot after $f$ in Definition 1?
Dec
30
comment Notation for vector composed of subset of elements of another vector
@JoshChen Ahh, I see. OK, Thanks.
Dec
30
comment Notation for vector composed of subset of elements of another vector
@JoshChen To make the point about the order of the elements in $\boldsymbol{y}(\boldsymbol{x})$, would it make sense to say something like, "the elements in $\boldsymbol{y}(\boldsymbol{x})$ are ordered according to their relative lexicographic ordering in $\boldsymbol{x}$"?
Dec
30
comment Notation for vector composed of subset of elements of another vector
@JoshChen That's a good idea. Thanks.
Dec
30
comment Notation for vector composed of subset of elements of another vector
@MichaelAlbanese Yes, that makes sense. Granted about the (17,...,17) issue. As for precisely how $\boldsymbol{y}(\boldsymbol{x})$ is constructed from $\boldsymbol{x}$, would you suggest that I just define it in words similar to how I did in the original question?
Dec
30
awarded  Commentator
Dec
30
comment Notation for vector composed of subset of elements of another vector
@SimenK. Yes, that's a better way of expressing the mapping. But, how can I express the mechanics of precisely what constitutes the vector $\boldsymbol{y}(\boldsymbol{x})$?
Dec
30
revised Notation for vector composed of subset of elements of another vector
added 34 characters in body
Dec
30
comment Notation for vector composed of subset of elements of another vector
If I understand you correctly, then I would say that different vectors, such as you mention, can be sent to differently dimensioned vector spaces. It's not important that all R^N vectors be sent to R^M for the same M. So, yes, it's not well defined, but what I'm writing here will hopefully make it more clear what I should have said.
Dec
30
asked Notation for vector composed of subset of elements of another vector